Back in Sun/Moon, I had this answered at https://pokemondb.net/pokebase/50959/what-is-the-highest-stat-possible?show=313243#a313243 -- let's see what changes in Sword/Shield.
For HP, Blissey is one of the species that was culled from the game and not included in the Galar dex, so it can't be used. In return, Dynamax was added as a mechanic, so currently a Dynamax Wobbuffet (the highest HP to survive the cull) reaches 1168. However, it's been advertised that Chansey and Blissey will be among the Pokemon returning in the upcoming DLC packs; once those are released, a Dynamax Blissey will top out at 1428 HP. Or, bending the rules in a way, while the player's scale factor for Dynamax HP ranges between 1.5 and 2.0 based on dynamax level (it's (30 + DL)/20), the scale factor in Max Raid Battles is dependent on the star level of the raid, with 1-star raids getting 1.4x HP and 5-star raids getting a whopping 3.0x, which is more than the player can ever get. So, supposing a Wild Area News event were ever released in the mold of Mewtwo, but featuring a level 100 Blissey in a 5-star raid after the DLC is released, that can have a maximum of 1953 HP (651 x 3, since it won't have any EVs as a wild battle). Too bad the players would never be able to see the numeric figures that go with Max Raid HP bars.
In Attack, nothing changed. Pikachu (of course), Shuckle, and Cherrim all survived the cull, as did a source of Huge Power (say, Diggersby) and the right moves to do what they did, but nothing that can improve on them. 14712 is still the limit there. (It would increase slightly to 14728 if Pikachu had a way of legally executing Transform, since that way it could transform directly into Shuckle and still get the Light Ball boost, but it doesn't.)
In Defense, I suggested using a Smeargle, which is no longer possible. But the basic skeleton is still there: you want something with Substitute (to make Transform repeatedly fail), Guard Swap, Skill Swap, and a defense-boosting move. Guard Swap actually became a TM in Sword/Shield, giving it more widespread distribution than before, while Skill Swap is a TR and Substitute is of course a universal TR. Mr. Rime can do all that for example, using Barrier as its defense boosting move. It's slightly inferior to Cotton Guard in having to be used 3 times to max out the stat instead of 2, but there's easily enough time to handle that. Then for the ability, Furfrou was culled as a donor of Fur Coat, but Alola Persian is still there (at least now that you can transfer one up from Bank) and gets you to the same final total, 9808.
Special Attack works out similarly to Attack: Pikachu is still there, as is Power Split. Plus and Minus still exist in the region courtesy of Toxtricity, and despite being only 1.5 instead of 2.0, they're still the best multipliers we can get for that stat out of the ability slot. What's different is that we no longer have megas or primals, and Pokemon like Deoxys and Xurkitree have also been culled. The highest surviving raw stat we have there is 482 from White Kyurem, which means that repeatedly transferring to another Pokemon with Power Split can only lift it as far as 481 (and in fact, for this exercise we actually need Pikachu to Mimic Power Split and be the one using that move to repeatedly siphon from Kyurem). Because of the lower starting point, we can't help but finish lower: the best that was possible in the SM version was 6408, but now the limit is only 5772.
Special Defense is a goofy one. The old solution requires Clamperl (for Deep Sea Scale, the only item that can give a 2.0 multiplier in this stat), but that's been culled so we can't use it. The next-best item choices are Eviolite and Assault Vest, both for 1.5x. However, we also gain something that wasn't accessible before: an ability that provides a straight boost to Special Defense, namely Ice Scales (from Frosmoth). So what ends up making the most sense is using Shuckle as the stat gouger directly: by doing that it can use its full 614 in the raw stat, whereas repeated Power Splitting can only lift someone else up to 613. Start by getting stat boosts (possibly with Contrary Shell Smash) up to +6, have someone Skill Swap Ice Scales over to Shuckle after it's done boosting, then we have to get the Assault Vest onto Shuckle somehow. It doesn't learn Thief naturally to steal one, and a Shuckle with Mimic can't also have Contrary to make the boosting process easier. Further, attempting to Trick one runs into a problem, in that Assault Vest normally stops you from using status moves, including Trick itself. However, there's one Pokemon in the Galar dex that can ignore that restriction: Swoobat, who gets the Klutz ability, allowing it to ignore the effect of its item but still move it over with Trick. Finally, the last step of preparation is to use Sandstorm, which naturally boosts Shuckle's Special Defense since it's a rock type. Putting that all together, the final stat ends up being 11052, much higher than the previous version was capable of (7356). It even slightly tops the XY mark, which used triple battles (something that no longer exists) and replaced sandstorm with double Cherrims each with Flower Gift in sun. That one only reached 11034, the 18-point difference being attributable to having to use Shuckle to Guard Split Clamperl up to 613, instead of being able to use its own 614 directly.
And finally, Speed is still an awkward matter of definitions. We still have Ditto, Quick Powder, Speed Swap, abilities like Surge Surfer or Swift Swim, and Tailwind, but what we don't have is Deoxys. Instead, the fastest Pokemon that made the trip was Ninjask, for a raw speed of 460 instead of 504. Putting all the bells and whistles in place from that lower starting point is enough to reach 14720, but the same proviso as before still applies: there is a hard speed limit of 10000 that higher stats will be pushed back down to, and anything that actually hits that 10000 limit will have its effective speed reduced further, and only act as though it has 1808 speed.
