C Tier probably. It didn't get used during the tour and there is probably a reason for it. The only niche use I could see for it is something like Marvel Scale Milotic safely switching in to a Will-O-Wisp and coming out with positive health. But, even then, why wouldn't you just use Leftovers for most things, or Flame Orb for anything that wants statuses, like Guts?
B+ tier. While currently its best abuser is the obvious Night Slash Unburden Sneasler, there are certainly other benefits to getting +1 Attack, especially if you happen to have someone with a Slicing move that doesn't normally have access to tools like Bulk Up or Swords Dance. This would be rated higher if it was a more reliable option for Pokemon other than Sneasler.
SSS Tier B- Tier. As fun as that was to use in the tour, looking at the damage output, even from something like Bax, it doesn't really seem like the damage output from this item is worth it. Sure the multihit effect breaks Sash or Sturdy, but a lot of things have enough bulk to take the 125% damage. On top of that, I don't know how the interaction works with moves like Draco Meteor (e.g. does it drop the Sp. Atk twice, once after each hit? That doesn't seem useful at all). Probably are some good uses for it, but doesn't seem like it packs quite as much punch as it sounds.
A Tier. Sun will always be strong, and this damage boost will be nice. While less than that of Life Orb, no recoil is always nice. Not only would it pair well with fast Proto or Chlorophyll mons, but it probably also allows Pokemon that normally don't fit well on Sun teams to help fill an offensive hole in some teams.
B Tier. There is probably a lot more potential for this than I explored, though a Fire type Flower Trick was interesting to see. The Fire type could be used well offensively, but finding a good Pokemon that has a Grass type coverage move to change may prove difficult.
B- Tier? Did not see this during the tour, so hard to judge. The biggest difficulty here is that it is more common than not that your opponent will always have non-damaging moves to throw at you, making the fact that the damage meter resets if you don't take damage on consecutive turns something working against you. Probably has potential on certain bulkier Pokemon, but unless you plan on switching into something like a Population Bomb you likely won't make it all the way to that 2x modifier.
B Tier. Single use Beast Boost (but not for Attack) could have some good use. I suspect that the Special Attack and Speed variations will be the more useful ones, but I can see how certain defensive or stall structures may want to see their defenses increase when an enemy gets chipped away.
A+ Tier. This thing is insane on something like E-Speed Dragonite, and can probably work well with moves like Fake Out. Normal+Ground is now almost perfect coverage (thank your Corviknight or Skarmory for keeping you safe) and there are lots of strong Normal-type moves that can benefit from this power boost.
B- tier. Tinted Lens, but just for the Ice vs Water interaction, feels somewhat mediocre. After all, Ice is still resisted by a few other types, and it isn't nearly as strong as Freeze Dry's Super Effectiveness against them. Could something use this well? Sure. But do Ice types have better held item to choose from? Absolutely.
B+ Tier. While not fully in the works, a discussion of what Pokemon have interesting moves that get this +1 priority is a longer list than you might expect. Pika-clones have access to Nuzzle, Ribombee has Draining Kiss, Breloom has Technician Bullet Seed, Maushold has Technician Population Bomb, Forretress has Rapid Spin, etc. Moves like Snarl or Chilling Water could also be useful utility to reduce an opponent's attacking stat before you take the hit. The BST restriction obviously keeps this item reasonable, as even expanding the BST to 500 would probably jump this item to S tier. But as it stands, this item allows for some interesting Pokemon to get a time in the spotlight as they use this.
C Tier. I hate to rate this so low, but it is more or less a fact. The big issue is that besides Garganacl, there are no good fully evolved Rock types. Sure you have Pokemon like Lycanroc-Dusk, but they would rather run Life Orb to deal more damage, even if it means the risk of being burned. Honestly, if the restriction on this item was expanded to include more Pokemon, it could probably be a really great item with some defensive niche. Alternatively, if the item also gave Rock types access to the move Recover there could be some viability there. Unfortunately, with neither of those being the case, this item will most likely never be used well because no good Rock types want to use it.
B- Tier. This one is tricky, there is potential here but this is not an easy one to use. Using a Psychic move to pass off the stat drops from moves like Close Combat or Leaf Storm could be interesting, but the catch is that you are still using a Psychic-type attack. I'm not sure if you know this, but the Psychic type isn't quite as good offensively as it used to be. There are a lot of strong Dark and Steel types that can just eat the attack. The effect is interesting, but it also means you cannot set up with a Pokemon if you are planning on swapping the stats on to the opponent. You also have to find a fast Pokemon to use it if you want to steal the stat changes from a setup sweeper. I would love to see this used well, I just don't know if it can be.
B Tier. Similar to how Chien-Pao above is carried by Sneasler, this item is probably carried by the best Grass type in the game at the moment; Rillaboom. There are probably other good grass types that benefit from this pseudo-Regenerator effect. But Rillaboom is the standout option that is willing to give up its item slot, as it doesn't rely on Leftovers for recovery. There are probably several other grass types that could also use this but not many are good in OU for a reason.
and these lower BST mons are probably gonna want this over Loaded Dice most of the time. Also 
gets this, but its already pretty fast, especially if it boosts with Tidy Up, and it wants the reliably of Wide Lens over priority.
(Orangesodapop / Beebos)
(Mossy Sandwich / Gaboswampert)
(Yoshiblaze / PQRDG)
(Gekokeso / IceLevelIncarnate)
will probably be the best abuser, but every existing Sharpness mon wants scarf most of the time over a +1. On the flip side... Unburden 
to set Sun.
Ivy Cudgel to be a poor man's Hearthflame, or for Fire-types in Sun to run this with Solar Beam. Slightly weaker but more spammable Overheat with Sun up. Sun might be eating right out the gate.
Fazbear to take his place! Weird LO/Choice item hybrid, but gives Normal attackers some merit, even if Guts mons are still gonna run their usual orbs most likely. 
can relive his Tera Normal ESpeed glory days somewhat.
.
or 
can get some decent use out of it.
probably benefits the most from this and makes it an even better pivot.
