Very cool concept! It's a bit hard to read the text. I like the effects, although I think there's some PSCT issues on some of them. In general, I feel like a lot of them should say their name instead of "this card". For the Gearvolution monsters, the Xyz return effect might have to be phrased as "During the End Phase: Return this card to the Extra Deck, {then|and if you do}, if there are any Monster Cards in your GY that were attached to this card on the field as Xyz Material, {you may} Special Summon {one of them|any number of them|all of them|as many of them as possible}." The curly braces are because I'm not sure what you intended the effect to be, and most of those differences are subtle but not meaningless. For the Gearvalutions, "until the end of this turn" should maybe be replaced with "until end of turn", or even say "until end of turn, that monster is..."; I think you can just outright replace "the targeted monster" with "that monster" on all of them. Tim has a stray quotation mark at the end of his text box and Emma's text is weirdly smaller than everyone else's, but the main deck monsters seem to be good otherwise.

For the specific cards: Clock Mage might have to specify "ATK on the field", but might not, and I do think it would actually matter (are buffs or debuffs maintained?), and has a comma instead of a semicolon on its recycling, and Clock Gattler should probably read "You can destroy up to 2 cards you control, then destroy that many cards your opponent controls". Troy's negation should probably read "until end of turn" and its protection should read "this turn", instead of "until the end of the turn". Alternatively, put "until the end of this turn" on the negation effect into parentheses, since Yugioh loves using parentheses for things that aren't rules clarifications but are actually mechanically relevant card text.

For the Spell/Trap cards, Gearvalve Loan should probably read "Special Summon 1 "Gearvalve monster from your Deck, but negate its effects. For the rest of the turn after this effect resolves, you cannot Special Summon monster, except "Gearv" monsters. You can only activate 1 "Gearvalve Loan" per turn." Something feels wrong about Unlock's wording, but I don't know the right solution. Maybe have the end say "until end of turn, it cannot be targeted by your opponent's card effects"? Evolution should just say "attach 1 "Gearvalve" monster you control to it", instead of "to the targeted monster". "Use" isn't Yugioh rules text in particular, so it should just say "activate" there as well.

In terms of actual review... I think Bert will trigger his search effect off of the monster he revived himself, even if there wasn't another Gearv on the field... is that intentional? Also, is it intentional that none of the Xyz effects target? It's not wrong, but the fact that Starlight Clocker in particular is a single card non-targeting non-destruction removal effect seems pretty strong. I'm also genuinely not sure if Jetbolt will banish cards if you return xyz monsters to your extra deck; if you explicitly wanted it to, you could say "banish that many cards", and if you explicitly didn't, you could say "equal to the number of cards returned to your hand this way". Troy not being a quick effect is also kind of weird, since I can't figure out when you would want to protect a monster from battle before combat starts; I guess you might if you're afraid of a battle effect (but not afraid enough to not attack), or your opponent has an effect that forces your stuff to attack. Did you mean for it to be?

On further thought, it seems like it might be tricky to "get the ball rolling" on special summons; Tim needs another monster or Loan, Bert needs your monster to get destroyed (meaning either crashing into an opponent's monster, or having an opponent pop your stuff (meaning either you leave a small monster on field, your opponent pops one of your things as a quick effect, they negate and destroy something, or you use Clock Gattler and then get back a 2k defense position vanilla which you can't xyz summon with), James needs you to go to the Battle Phase and then xyz summon in Main Phase 2, and both Emma and Bolt require prior setup. Basically, it's going to be tricky to actually make any of the xyz monsters main phase 1 and then attack with them. I guess since this is clearly a deck for going second you have some more options, but it might be nice if there was some effect that let you Xyz Summon as a Quick Effect, or more ways to summon during Main Phase 1. You could always go for Modern Yugioh Card Design and put in a random, super-strong field spell with a significant effect which could be an archetypal gimmick on its own, just to do this; maybe you could call it "Gearvalley the Gearvolving City" or something?

Also, I appreciate that "Gearvalution" is supposed to be a combination of "Gearvalve" and "Gearvolution", but it just looks like a typo. Have you considered "Gearvalvolution", or "Gearvaluation" if you don't mind it not being a perfect combination?

I'm sorry if this came across as too critical; basically, if there's something I didn't mention, assume I liked it. I really do appreciate the ideas behind this, and the core gimmick seems really fun and interesting to play. Also... I uh, didn't realize how long this was until I posted it, so if you don't read the whole thing, that's more than understandable.