overview post of the new stuff relevant to BH:

A TALE OF HOW YOU'RE ABOUT TO LOSE (shed tail) - 50% HP sacrificed to switch and give the mon coming in a substitute.
this move is kind of busted. it enables offensive strats so ridiculously easily and shed tail + regen is stupid given how much progress it makes as opposed to the cost on the user. you cah shed tail with basically any fat mon, go to a booster and there's a very high chance you can just pick up a kill there and then.

FILLET OF FISH (fillet away) - cuts HP by 50% of maximum to give +2 atk/spa/spe.
personally i think this is just worse drum and smash. worse than smash because you're a lot easier to pick off/ imposter is a lot safer against you/you can realistically only use it once, worse than drum because you lack highly explosive killpower.

GCSE BIOLOGY (protosynthesis) - when entering with booster energy or in sun (elec terrain for quark drive), highest stat is boosted by 30%, 50% if speed.
i don't think this will see much use. imposter doesn't copy the protosynthesis boost, so theoretically you can use booster energy + proto with speed as your highest stat on drum sets to still keep the speed boost after being hazed, however i think unburden is better in every instance here. using with stats other than speed is pointless bc ruin abilities simply exist.

PRAYER BEADS BRACELET, A BALANCED ADD-ON (ruin abilities) - cut an opponent's stat by 25%. tablets cuts attack, swords cuts defense, vessel cuts sp.atk, beads cuts sp.def.
since these lower opposing stats by 25%, this correlates to a "33% boost" to your stat (ie. using beads means you deal 33% more special damage):
these are now the de-facto highest damage boosting abilities since they are boost every move on phys/spec without exception. the only exceptions to this are gorilla tactics, orichalcum pulse (bc it both sets sun and boosts the stat by 30%) and hadron engine (same as pulse but eterrain instead). adapt has the same boost on STABs but crucially doesn't reveal itself, so is better suited for mixed / mono-STAB / attackers that enjoy their sets being hidden.

DEFINITELY NOT ENGLAND (ori pulse and hadron engine) - sets sun and boosts atk by 30% / eterrain and spa by 30% respectively.
if you're using fire or electric nukes (like band zac-c for example), these are the best things to use for them, as you're effectively getting either a 1.95x boost or 1.69x boost depending on whichever one you use. pretty simple.

ME WHEN CLASH OF CLANS (ting-lu)
this thing is ridiculously bulky. 155/130/80 bulk makes it, if i'm not mistaken, probably the bulkiest mon ever. on top of being an ultra-fat ghost resist, it also has ground type for a stonewall to miraidon completely free of charge, and to top it all off even has dark as it's primary typing so you can run revdance to beat normalize caly if you have no counters. base 45 speed also makes it a great slow pivot. overall i expect this to see a lot of use just based on bulk alone.

DIEGO FROM ICE AGE (chien-pao)
this mon is a gen too late. it's basically weavile but base 135 speed, which would have been great last gen since SD sets would outpace and thus could destroy etern and zamac, however this is significantly less valuable here due to the presence of calyrex and zacian (on top of etern and zamac just generally being lower value too). unlike other fast but frail mons like base zama, it has 0 bulk with which to effective use strength sap, and despite life orb + swords of ruin basically ensuring you OHKO something if you hit it super-effectively, it's not strong enough to threaten basically any neutral target like slaking or neutral arc forms.

BIG BOZO (dondozo)
slightly less bulky than lu-ting (do you finally get the joke? looting? clash of clans? do you want a blue peter badge or something?) but comes with water type, effectively meaning you can run a fc water without needing waterceus. taunt slaking is everywhere rn so i think dragon tail/circle throw and just hope they aren't the right tera to autowin is necessary, otherwise i think this'll mostly be like last gen suicune where it just sits there and eats hits really well but doesn't do much else.

HE GOT CHINGED ON HIS ONES (ceaseless edge and stone axe) - these set spikes/rocks respectively if they hit. this effect is blocked by covert cloak.
new ways for defensive mons to make progress, with hazards that can't be bounced or taunted and that can be used by regenvest mons. ceaseless breaking caly-s's substitutes is big and just being able to pressure defensive mons for staying in against your defensive mons is really strong.

AVERAGE WARZONE PLAYER (mortal spin) - poison type, poisons the target and clears hazards if successful.
spin alternative which makes more progress but sets up the user less (no speed boost) and is blocked by steel types which are arguably more common than ghosts. i don't think it'll see massive use, especially when the offensive meta cools down and people start running -atespin again, however it's a nice other option and, as a regenvest user, you can punish your spinblocker more effectively with mortal spin than you can with rapid spin, as the main steels hate nuzzle but giratina doesn't mind too much.

GIANT HOOVER (tidy up) - ddance + defog, but also clears substitute on both sides.
this is interesting as a hazard clearing option as it's defog that you can use offensively, however i also don't really know what is ever going to use this as basically every ddancer in gen 8 either sets spikes or wants them. from a strictly hazard clearing perspective, defog is better because it has more PP and being blocked by not having a target is not too relevant in BH, however prank tidy up being self-targeting means darks can't block it which might be relevant in some situations. i can see the use case for some stuff that's like this, however said stuff isn't exceptionally relevant or is illegal at the current time.

OTHERWISE KNOWN AS A WMD (population bomb) - 10 hits of 20 base power. amount of hits calculated the same way as triple axel (90% accuracy check for each hit, must land the check to consider the next hit), makes contact.
this move has some really big damage potential, just based on the fact that it's 200 base power at max. it's definitely flawed despite this massive value, such as needing coil or wide lens to be actually reliable and instantly killing the user if they connect with helmet, however there are workarounds and it is used on some incredibly dangerous mons to good effect. most commonly it's seen on coil pixilate zacian with pads, however stuff like choice band normals and king's rock also exists.

YOU NEED A HGV LICENCE FOR THAT (gigaton hammer) - 160BP steel move, can't be used twice in a row.
this move gives zac-c another excellent option (as if it needed any) and is mostly just used as generic STAB to have on a set if you want to whack something really hard. it's excellent for offensive steels and the only good physical steel move since anchor and sunsteel have been removed, however zac-c is the only offensive steel currently. doesn't really mesh well with band sets tho.
there's also generic new STABs for certain types like dragon (glaive rush), fairy (magical torque), ground (headlong rush), steel (make it rain), fighting (collision course/combat torque), electric (electro drift), normal (hyper drill) but i don't think these are worth mentioning in their own sections as glaive, make it rain and headlong rush are all drawback moves and the rest are just generic STABs with high BP and decent secondary effects.