Cat will attempt to answer this question the clearest way I can
Psychic has too many mons to actually have a clear structure of, but like most types, they have patterns of mons that are pretty much so to say, staples. These are the Victini and the Psychic/Fairy.
Oh, and by the way, Screens Psychic does exist;
Screensusers used it to an appreciable extent last MLT, but balance Psychic is preferred in most cases due to its access to
very annoying slowtwins
Needs no introduction, it provides a way to deal with Steel-types which are super annoying to face for Psychic users. Its usually Heavy-Duty Boots due to Psychic teams generally having bad/no entry hazard control apart from Hatterene/Defog Latis. Choice Band sets favor the brave, especially when you have Hatterene+Defog Latias in your team.
Partially had a resurgence due to Galarian Moltres [which it deals with better than Tapu Lele], provides entry hazard control in magic bounce but you have to be gutsy as some Entry Hazard setters like Landorus-T and Jirachi are ones Hatt wouldn't want to mess with. Its notorious for being able to solo Dark teams with a set of Trick Room, Calm Mind, Draining Kiss, and Psyshock. It doesn't have Terrain unlike Lele though; however you can deal with Bisharp and Choice Band / SD Weavile with Colbur Berry Slowbro. Sometimes, people run both Fairies in Psychic teams, however, this comes at a cost of usually not running a Stealth Rock user.
Provides Psychic Terrain and is notorious for being able to steamroll or even clean types late-game. Modest Choice Scarf Lele is sooo Powerful. However, it has bad things going for it too; Its slower than Choice Scarf Blacephalon and Zarude, both of which threaten Psychic teams immensely. Btw if you use Tapu Lele you can use the Ghost berry on Slowbro to deal with Dragapult, as Bisharp gets neutered by Psychic Terrain, Scarf Weavile gets walled by Slowbro, and Band Weevil is outsped by Scarf Lele
Its Psychic's physical wall, walling an obscene number of threats including Excadrill, Urshifu-R, (non Choice Band) Victini, and Barraskewda. There's a reason why Choice Band Exca runs X-Scissor; its to 2HKO this thing. Teleport is its defining trait, as its ability to forces switches from Physical attackers allows it to Teleport out to answer the opposing teams switch-in. Since it has extremely good def, people stick a Ghost or Dark pinch Berry (Kasib/Colbur) to lure and delete Dragon Dance Dragapult/SD Bisharp or Weavile.
Those 3 should almost be in every balanced Psychic team [and is where you start with, most of the time], and you can use the following to complement them:
Is the special wall, removes Tspikes [which makes Dragons cri :(] and can sort of handle Blacephalon and Aegislash, while also exerting pressure on teams such as Steel and Fairy. Its usually using Assault Vest
Sets Stealth Rock and can be a decent Scarf user [notably creeping Scarf G.Darm, which Lele can't] or temporary spdef wall [checks Hatterene and Lele which Galarian Slowking can't always do]
Usually a Defogger, but its not so good in that department unless you have Myst Fire to threaten the Hazard Setters. It does have Healing Wish though, which greatly helps sweepers like CM Hatt / CP Mew / Stuff. It can rarely run a Weakness Policy Set with CM / Agility / Stored Power / Recover, but that's mainly for trolling Electric.
Offensive Calm Mind user. CM + 3Attacks is super scary to face, having very limited switch-ins. Some people stick a Colbur Berry on it to combat Goltress, though.
can utilize Cosmic Power sets, entry hazard sets, and is cat. If you're using CP Mew though, pairing it with G.King is ideal as G.King removes Tspikes which cripples it.
Other options that might be worth it to round out the team:
You hate Kyurem and Choice Band Excadrill + you want a Stealth Rock user
Pair it with Hatterene and see both kinda be really scary. Unfortunately, aside from nope-ing Ghost-types like Spectrier and Expanding Force, Tapu Lele is better in almost every other way.
Annoying brain cell that, unlike mew, isn't bothered by Status. Don't forget to speedcreep for Toxapex though!
The thing with Celebi is it can't switch into Urshifu-R nor Excadrill, as they have U-turn and X-Scissor which deletes Onions. It doesn't even reliably switch into Barraskewda's Crunch, iirc. It can be an alternative Stealth Rocks setter though, with the perk of not automatically folding to Electric-types.
Focus Sash for Volcaroo and a lot of threats. And outspeeds Cinderace.
People run Scarf in this thing apparently, Lunar Dance is notable, though is it really an upgrade over H.Wish? Access to Ice beam is also a thing. It can run a CM set due to its bulk and access to Recovery + Moonblast, but this seems inferior to Mew / Reuni. Can set TR too.
You get one (1) White Queen stamp of approval. Superpower/Knock Off/Rest/Stalk seems like the best set for it, it lets it deal with Aegislash and some ghosts, this mon is not explored that much tbh.
or
+
Screens Psychic?
I hope this rambling helps you a bit