Progress by Aquila
I like this, it is pretty straightforward with the neat "once per game" twist (which is similar to Aquila's Prospects).
Without that it would be strategically boring, you just wait until enough tokens are on the card and then take them.
Now you have to think about when you need the tokens most (early on to get your engine running vs. late for a mega-turn), you naturally want a lot of them and you have to consider when your opponent(s) will want them.
A possible alternative that comes to mind is to make the trigger "costing 5 or more" and then do the halving.
Tulip by Lurker
The idea of a Victory card that is worth 1 per copy left in the Supply is an old one so being able to return them to the Supply for a benefit is neat.
Gem Mining by King Leon
The most creative and complex card that implies a minigame.
I understand the rationale behind limiting the slots to a row/column and the spillover (bootstraping the minigame, even if Bob did not want to go for the gems at all, if Alice gets some and B gets some remaining gems he might go for them after all) but it does not feel natural.
On the other hand the more natural "put them wherever you want" is too easy and does not lead to tricky decisions (do I really want to take 4 gems, finish the column, get a $5 but gift 2 gems to Bob?).
It is hard to judge details like the gem distribution and the bonuses without having played with the Event. If Leon or somebody else ever tries this out it will likely have to get slightly tweaked anyway given how many paramaters there are.
Salesman by hhelibebcnofnena
I like the "Villager cantrip" basis of the card. It is a bit like Patron, sometimes you might be able to save the Villager.
But the rest is bad. In order to make Salesman work you need several copies, so you will save the villagers less often and then the card still produces on average less Coffers than Baker. Ignoring player interaction, Salesman is to Baker as Native Village is to Village.
With Throne Room (variants) in the Kingdom this downside could be compensated for by the relatively more Villagers you get.
Prospector by mail-mi
Looks sound and well thought out. Quick Treasure trashing often makes you want to go for an early Gold and the Coffers help you do get there. There are also potential tricks like, while readjusting your deck in the middlegame, trashing a Silver, buying a Gold and getting a Coffers and a VP. Importantly there is no abuse potential as this does not seem like something which you can/want to do consistently.
A small detail, I wonder whether the card could get away with "when you gain a Gold".
Botanist by NoMoreFun
I like the Cultist-like idea of a "half-terminal" and the self-limitation of the card (you cannot mindlessly flood your deck with them) but I feel like the latter is too harsh. So perhaps the card is not overpowered if you get rid of the non-Botanist Action card restriction. The worst that can happen is that, ignoring player interaction for the sake of simplicity (Alice buy a Botanist but then Bob plays 2 Botanists, thus stealing "Alice's" Villager) , the card is always at least once non-terminal.
Casino by Commodore Chuckles
This is similar to Spice Merchant, with some Coin-spike or megaturn potential. Also neat in non-mirror Garden games.
Uprising/Commons by 4est
Uprising is far too good and will only lead to degenerate play. For example, why should Alice trash an Ironmonger if Bob can pick it up so cheaply for 5D and get to immediately play it. This would be like Summon but this turn instead of next.
So if nobody has an incentive to put an Action on Commons only Copper will land there. All that achieves is an auto Copper pile-out, e.g. in a 3P game after 13 turns.
Hogwarts by majiponi
I guess this is just intended to be a pun as tapping cards in Dominion makes no sense (unless you design a Duration card which does not do something at the start of the next turn but during the turn and have to somehow mark that it has already done something) and it is not explained what the Mana can be used for.
Ring of Power by faust
This does not match the parameters of the contest, a binary private variable that can be triggered by other players has nothing to do with amassing common resources. Ignoring that, the card provided neat payload for a deck-drawing engine and in Kingdoms with gainers you can gain enough Silvers or other $3s to "survive" until then. Or you gamble and rarely have a discard pile.
Playwright/Theater by Fragasnap
Non-terminal Gathering cards and especially cantrips are problematic. This is smartly mitigated via the split pile (and the high cost respectively opportunity cost in the case of the Duchy gainer; not all decks can deal with that).
The cards seem quite swingy though, whoever is able to first play Playwright and then Theater will likely get a huge pile of VPs.
On the other hand you could argue that this large amount of VPs is necessary to make players go for these expensive cards at all.
Runner-up: Gem Mining by King Leon
Winner: Progress by Aquila