For my hope, too, grows ever stronger
Powered Up! : An explanation of Power Items in BBP
Power Items are mostly known on cartridge as subpar items, aiming to facilitate EV Training but outclassed by Hordes in Gen VI or Poké Pelago in Gen VII. They are a bit more useful in BBP due to them increasing the stage boosts of stat-boosting moves. Now, let me explain: there are 6 Power Items. The Power Weight, Power Bracer, Power Belt, Power Lens, Power Band and Power Anklet are linked to HP, Attack, Defense, Special Attack, Special Defense and Speed, respectively, just like in-game (but unlike in-game, there are no EVs here!). Let's focus on everything but HP and Speed for now.
Power Bracer/Belt/Lens/Band halve your Speed, but in return they grant a +3 stage boost and +1 priority to a move that boosts the corresponding stat. For example, Iron Defense boosts Defense by 2 stages at +0 priority, right? Well, equip a Power Belt and now you're at +5 Defense, and you act at priority +1 when using Iron Defense! More of an offensive type of person? Equip a Power Bracer, use Work Up, and now you're at +4/+1 (the item only boosts the corresponding stat), likely before your opponent could act as well!
Power Weight (linked to HP) increases the recovery from recovery moves by 50%, and Power Anklet only reduces your Speed by 25%, adds a +3 stage boost/+1 priority to Speed-boosting moves (like Agility) and increases your Accuracy based on your current Speed.
Using Power Items can be very beneficial either from an offensive standpoint, to quickly gain enormous stat boosts, with Swords Dance for example, to overwhelm the opposition with devastating attacks. A slow-ish Quiver Dance user like Lilligant can try to quickly gain stat boosts this way. They can also put in work from a defensive standpoint to effectively wall an opposing Pokémon, such as Slowbro using Amnesia to patch up its weaker Special Defense with +1 priority. Power Anklet can find its use with Pokémon having a plethora of strong but inaccurate moves like Focus Blast, Zap Cannon or Dynamic Punch in tandem with Agility. Power Weight also works with offensive recovery moves like Giga Drain, so an already tanky Pokémon (Necturna using Horn Leech for example) using it could see its lifespan dramatically increased!
Power Items are often overlooked, therefore using one in a last-'mon situation can really allow you to either make a surprising comeback or secure a win, depending on how you decide to use them. There are six of those, so the possibilities are actually quite wide!
Unfortunately, they are also pretty gimmicky. Since the opponent is always aware of your item in BBP, it is easy for them to look through your strategy and try to counter it. Your Pokémon also has to sacrifice its item slot, whereas it could have used a more "goodstuff" item like Rare Candy or a type-boosting item.
All in all, Power Items are an unexplored route in BBP. While more practical items like Rare Candy, Expert Belt or a Z-Crystal might be generally more useful, situations arise where they are the perfect fit and can be absolutely devastating for your opponent. Don't be afraid to power up from time to time!