So I've been starting to work harder on being able to handle 6 star raids on my own. I'm taking the time to be more conscious about type matchups in terms of the moves used by tera pokemon, which is obviously much better than simply focusing on the tera type. My biggest goal is to someday put together a list of specific pokemon/move sets, etc that I find work best against specific tera raids. It may already exist, but the discovery is the fun part for me.
That being said, here is what I've found personally works best for Aqua Tauros raids. Any suggestions for improvement would be nice, though my current system has not yet failed me.
To start, the moves used by Aqua Tauros are as follows (according to Serebii):
Wave Crash (Water. Physical)
Close Combat (Fighting, Physical)
Surf (Water, Special)
Headbutt (Normal, Physical)
With bonus moves Bulk Up and Rain Dance.
Azumarill is a good choice here, of course, because it will resist three of the four attacks. But I've seen my fair share of belly drummers get bonked.
The BEST pokemon I have found to deal with Aqua Tauros is Brambleghast. It's move pool is honestly extremely lacking, but with a little effort, the little tumbleweed simply will not die to Tauros. It's Ghost typing completely eliminates Close Combat and Headbutt from being used. Its grass typing make is resist the two water moves as well. And Tauros prefers Physical moves to Special ones, so the only moves you'll see used by Tauros are Wave Crash, Bulk Up (in my experience not often), and Rain Dance. Wave Crash is a strong move, but it comes at a price for Tauros due to recoil damage.
I've maxed out EVs in Special Attack as well as given Brambleghast a lot of Defence EVs as well. I typically have it hold a metronome and the moves it currently has are Phantom Force, Giga Drain, Defence Curl, and Hex, though I may change the last one. My set up is basically to use defence curl once or twice, then spam Giga Drain. Tauros spams Wave Crash. does very little damage, and hurts itself in the process. Meanwhile I progressively get stronger up to a point and heal myself at the same time. I don't need to terastalise, either, and I don't want to due to the ideal dual typing.
The only time this strategy may not work is if Tauros is a tera type that is Steel since it would then resist any move/type of move that Brambleghast can work with, but I haven't dealt with that yet. I have dealt with neutral tera types (Electric, Fairy), and Brambleghast has won both.
So if you end up with an Aqua Tauros and you don't want to have to deal with random that bring in pokemon with Normal. Steel, Fire, Dark, Ice, Rock, or Ground types (often I see Meowscarada without its hidden ability, and I just dealt with a team with two Kingambits on it, oof! It also had a belly drum Azumarill who unfortunately also got bonked, I suspect to a stray critical hit.)
Thank you for coming to my Ted Talk.

Brambleghast
Grass/Ghost
Wind RideInfilitrator
55/115/70/80/70/90

*EDIT: The current maximum possible HOME GO Dex number is now:

( 771 )

(if I missed something, let me know!)

edits:

2023
Mar 29

• Cutiefly and Ribombee were announced officially by Pokémon Go on Twitter, and so will increase the Maximum Possible Home Go Dex Number by 2 on (if I got my math right) April 3 at 5pm EST (or April 3, 10pm GMT; or April 4, 10am GMT+19) i.e. basically at 10 am local in New Zealand / Asia Pacific regions

Mar 28

• Several upcoming Pokémon were leaked but until they are confirmed via announcement or data mining, I’ll just leave the link.

Mar 10

• Regidrago was added to the game, but there have been significant errors with people being unable to join and/or catch. However, as at least one has been sent to home, it has increased the maximum HOME GO Dex number by 1.

Mar 8

• Bruxish was added to the game, and thus increased the Maximum HOME GO Dex number by 1.

Mar 3

• Apologies for the delay, I overlooked the fact that Hawlucha was added to the game as a Mexico-exclusive regional since Mar 1, and thus increases the maximum possible HOME GO Dex number by 1 (thanks for the heads-up cooptimesudoku )

Feb 28

• Regieleki was announced to be coming to the game.
• Steenee has been teased on the new app loading screen.

Feb 27

• Gimmighoul can now be caught, AND can theoretically evolve into Goldengo… but because it (and its evolution) still cannot be sent to HOME, it still does NOT yet increase the maximum possible HOME Go Dex number.
• Added the two newly released Pokémon to Paldea’s list, as they were released in Scarlet and Violet (but not in Pokémon Go)

Feb 10

• Kleavor was datamined.**

Feb 1

• Kecleon can now be sent to HOME again as the restriction on it has been lifted (and the HOME Maintenance has ended).

2022

• Added speculation for Paldea pokemon that are known to evolve from pokemon already released in Go. These pokemon could maybe, in the future, be evolved in Scarlet or Violet before their Paldean evolutions are released in Go; and thus increase the maximum possible HOME GO Dex Number early, like a few Hisuian Pokémon already can.
• Added new section thanks to help from relikter: Announced/Datamined/Theorized

 

Out of the current 1010 total possible Pokemon that could be in a Pokedex:

A. (-22) All 22 Mythical pokemon never count toward the Home Go Pokedex number, even if it is available and you send it up. (This includes Meltan/Melmetal!).
B. (-3) 3 Pokemon (Spinda, Gimmighoul, and Goldengo), are currently not able to be sent to HOME even though they are in Go and would otherwise count towards the HOME Go dex number.
C. (-214) There are 214 pokemon that are fully unavailable to have a Pokemon Go mark, because they (or their pre-evolutions** ) are not yet made available in Go

So, with a little math: 1010 - 22 - 3 - 214=

771 Pokemon that CAN be registered in Pokemon HOME’s Go Pokedex.

**Some pokemon--currently Wyrdeer and Kleavor--Can have a Pokemon Go mark in HOME even though they are unreleased in Go. This is achieved by sending the pre-evolution Go Pokemon--Stantler and Scyther--to another game (such as Legends: Arceus) and evolving them. (See more under Theorized!)
 

Lists of all Unregisterable Pokemon***

(If a pokemon is not listed below, it can be registered in the HOME Go Dex.)
 
(A) All Mythicals (22) do not count towards the HOME’s Go Dex number
-Mew, Celebi, Jirachi, Deoxys, Phione, Manaphy, Darkrai, Shaymin, Arceus, Victini, Keldeo, Meloetta, Genesect, Diancie, Hoopa, Volcanion, Magearna, Marshadow, Zeraora, Meltan, Melmetal, Zarude
(B) 3 available pokemon cannot be sent to HOME right now
-Spinda, Gimmighoul, Goldengo
(C) 214 non-mythical pokemon cannot have a Go mark in HOME due to being unreleased (if name bold, it is announced but not yet in the game). (2 + 7 + 25 + 75 + 2 + 103 = 214)
(2) Unova:
-Larvesta, Volcarona
(7) Kalos:
-Skiddo, Gogoat, Honedge, Doublade, Aegislash, Carbink, Zygarde
(25) Alola:
-Cutiefly, Ribombee, Wishiwashi, Mudbray, Mudsdale, Bounsweet, Steenee, Tsareena, Passimian, Sandygast, Palossand, Pyukumuku, Type: Null, Silvally, Minior, Komala, Turtonator, Mimikyu, Drampa, Dhelmise, Necrozma, Poipole, Naganadel, Stakataka, Blacephalon
(75) Galar:
-Grookey, Thwackey, Rillaboom, Scorbunny, Raboot, Cinderace, Sobble, Drizzile, Inteleon, Rookidee, Corvisquire, Corviknight, Blipbug, Dottler, Orbeetle, Nickit, Thievul, Gossifleur, Eldegoss, Chewtle, Drednaw, Yamper, Boltund, Rolycoly, Carkol, Coalossal, Applin, Flapple, Appletun, Silicobra, Sandaconda, Cramorant, Arrokuda, Barraskewda, Toxel, Toxtricity, Sizzlepede, Centiskorch, Clobbopus, Grapploct, Sinistea, Polteageist, Hatenna, Hattrem, Hatterene, Impidimp, Morgrem, Grimmsnarl, Cursola, Milcery, Alcremie, Pincurchin, Snom, Frosmoth, Stonjourner, Eiscue, Indeedee, Morpeko, Cufant, Copperajah, Dracozolt, Arctozolt, Dracovish, Arctovish, Duraludon, Dreepy, Drakloak, Dragapult, Eternatus, Kubfu, Urshifu, Regieleki, Glastrier, Spectrier, Calyrex
(2) Hisui:
-Basculegion, Enamorus
(103) Paldea:
-Sprigatito, Floragato, Meowscarada, Fuecoco, Crocalor, Skeledirge, Quaxly, Quaxwell, Quaquaval, Lechonk, Oinkologne, Tarountula, Spidops, Nymble, Lokix, Pawmi, Pawmo, Pawmot, Tandemaus, Mausehold, Fidough, Dachsbun, Smoliv, Dolliv, Arboliva, Squawkabilly, Nacli, Naclstack, Garganacl, Charcadet, Armarouge, Ceruledge, Tadbulb, Bellibolt, Wattrel, Kilowattrel, Maschiff, Mabosstiff, Shroodle, Grafaiai, Bramblin, Brambleghast, Toedscool, Toedscruel, Klawf, Capsakid, Scovillain, Rellor, Rabsca, Flittle, Espathra, Tinkatink, Tinkatuff, Tinkaton, Wiglett, Wugtrio, Bombirdier, Finizen, Palafin, Varoom, Revavroom, Cyclizar, Orthworm, Glimmet, Glimmora, Greavard, Houndstone, Flamigo, Cetoddle, Cetitan, Veluza, Dondozo, Tatsugiri, Annihilape, Clodsire, Farigiraf, Dudunsparce, Kingambit, Great Tusk, Scream Tail, Brute Bonnet, Flutter Mane, Slither Wing, Sandy Shocks, Iron Treads, Iron Bundle, Iron Hands, Iron Jugulis, Iron Moth, Iron Thorns, Frigibax, Arctibax, Baxcalibur, Wo-Chien, Chien-Pao, Ting-Lu, Chi-Yu, Roaring Moon, Iron Valiant, Koraidon, Miraidon, Iron Leaves, Walking Wake
 
*** Some non-mythical Pokemon that do not currently contribute to the maximum possible HOME GO Dex number are either officially Announced, Datamined, or otherwise Theorized to be made available soon. Some of these are detailed below; and when the pokemon is released, its corresponding postulation will be removed.

Officially Announced but not yet in the game

• Poipole, Naganandel, Stakataka, Blacephalon, and Necrozma were teased by Pokemon GO on Twitter
• Steenee has been teased prominantly on the new app loading screen, implying Bounsweet and Tsareena too.
• Regieleki was announced to be coming to the game.
• Cutiefly and Ribombee were announced officially by Pokémon Go on Twitter, and so will increase the Maximum Possible Home Go Dex Number by 2.

Datamined info that might signal a Pokemon's approaching availability

• Kleavor model was datamined. Kleavor could already be deposited with a Go mark in HOME, but this signals it might soon be able to be evolved in Go.

Theorized

• In the future there could be pokemon that would be unavailable in Go while still available with a Go mark in Home, by taking the pre-evolution Go pokemon to Pokemon Scarlet or Violet and evolving them before the evolved pokemon is actually released in Go. These pokemon would then increase the HOME GO Dex number prematurely. A list of them I'm aware of would be Annihilape (with a Primeape from Go), Farigiraf (with a Girafarig from Go), Dudunsparce (with a Dunsparce from Go), and Kingambit (with a Bisharp from Go).