A good bit late. Oops. Let's get this show on the road, then!
Note: If your wording is messy or unclear, I tried to clean it up. Hopefully this didn't impact anything you're going for.
Dog Breeders - Ally
At the start of your turn, or directly after playing an Action, you may spend an Action and a Favor for +2 Cards.
An interesting Ally that benefits both BM and engines in two completely distinct and separate ways. Village + Underling with this becomes basically Village + Smithy with a lot more lenience due to being able to save the Favors for future turns and not spend them immediately. Where I think this shines though is in a deck with minimal +Actions. There, every Action is more valuable, and spending it for Cards is a risk you have to consider taking or choosing not to. Nice work!
Contender
Queen's Court - Action, $5
Choose one: gain up to two differently-named cards costing up to $4, or you may play an Action from your hand twice.
A nice Workshop variant/Throne Room. I really like this card as Ball put into card form, but even without the Throne Room effect, it's probably pretty powerful. With it, it effectively removes the Throne Room stack of doom problem all together as you can just Queen another Queen's Court for lots of gains. I want to like this, I do, but it's too busted at $5. Might still be at $6.
Smithy Village/Goldsmith - Action, $4; Action-Duration, $6
+1 Card, +3 Actions
You may let all players trash a card from their hand.
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Now and at the start of your next turn: +2 Cards, all players may discard a card for +1 Card, and you may discard a card for +1 Action.
A split pile based around giving out bonuses. Smithy Village easily draws comparisons to Port and Bishop because I like comparing cards to existing ones in that you get net 2 extra Actions added to your deck and can let everyone trash. This seems pretty balanced compared to both of those. The upside feels like enough to balance out the downside of having it tied to one card instead of spreading your villages among two cards. Goldsmith works as a weird form of draw that I really have nothing to compare it to, and honestly? I really like it. Good but by no means busted, the free sifting to your opponents and ability to make it non-terminal (or even a village) roughly balancing each other out. Right at home as a $6 cost. Good work!
Contender
Two-Faced Assistant/Banned - Action-Duration, $4
+1 Card, +1 Action
At the start of your next turn: +2 Cards, then look through the discard pile of the player to your right and put the Banned marker on whichever non-empty Kingdom card pile they have the most copies of in their discard.
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You can't buy or gain any cards from this pile. At the end of your turn, remove this.
Double Caravan, but limits your ability to buy whatever pile your opponent is going for if you use even one. ...I'm gonna be honest, this seems a bit too good compared to Caravan on boards with good variety, and on boards without, it suffers the Tournament problem of not being fun to play with but a necessary buy because it's effectively a delayed double-Lab. I want to like this, and I can tell you put a good bit of effort into it, but there's too many problems with it for me to be able to say it's a good card.
Coach - Action, $5
You may gain an Action costing up to $5 other than Coach from the Supply and play it twice. Each other player may discard two cards from hand to gain a copy of it or a Horse to their hand.
This feels... monolithic. Cards that can gain $5-costs usually have some restriction to prevent them from mass gaining $5s too quickly (Artisan costing $6, University costing Potion, Horn of Plenty only activating when you have a good amount of uniques, War Chest preventing you from gaining the best $5, etc.) Your opponent being able to gain a copy of the card to hand for two cards from hand is... a fine cost; it'd make it alright, a bit weak solo, but would go up in power as your opponent lost cards from their hand; but being able to immediately Throne the Action you just gained kills any semblance of balance this may have had.
Night Market - Action/Duration, $4
The next time you gain a Curse in your Buy phase, trash this. At the start of each turn this is in play, +1 Buy, +$1. | While this is in play, you can't buy Provinces.
Solid! Looks fun to play around the restriction of when to trash this so that you get the most Buy and Coins out of this you can, but are still able to buy Provinces. Having it still use "While this is in play" is nice because you can use the Buys and Coins it gives you after you buy a Curse that turn. One interesting aspect of this that I don't think was considered is that you can shut your opponent out from buying Provinces if you drain the Curses, but I actually think I like that. Given that there's a good amount of alt-VP and ways to threepile, being stuck without Provinces isn't the death sentence it seems like at first glance. Overall, a very dynamic card with lots of ways to play it. Nice work! I do agree with segura that this would probably be better at $3, but given how much this card does right, I think a slight mispricing is negligible.
Contender
Slumlord - Action, $5
+3 Cards, +2 Actions
This turn, you can't play Actions costing $5 or more from your hand.
Simple yet strong. Very much a powerhouse in the earlygame when this may be the only $5 you have, but being unable to play other copies of itself is a balanced restriction. Seems very nice in a BM game where your draw is short anyway. My only concern is that this seems too powerful with cost reduction, and with being able to chain up copies of itself after just one Bridge play... this might be too good with cost reduction. A clause to make it so that you can't play Actions costing as much as this or more might be necessary, but good card aside from that nitpick.
Shady Market - Action, $5
+2 Cards, +1 Action, +1 Buy, +$1
This turn, you must spend all your Buys.
Short, simple, and sweet. One of the rare few cards to use "must" in this contest and does it well. High skill cap... on a good amount of boards, with playing around having to add a bunch of low-cost cards or Copper to your deck a key feature of this card. Or just get a bunch of money so the buys are a benefit and not a hindrance! Big concern for this one, and it's that you can burn all your Buys on 0-cost events such as Advance to completely ignore the downside of this. Comparing this to other cards, is the quality of this over Lab to the point where that's a game-breaking interaction? I say no, and what we have here is a card that's more swingy in terms of power level yet still just as fun. Nice work!
Contender
Royal Forest - Victory-Reaction, $5
2 VP
When you gain a card, you may discard this to gain a differently named card with the same cost.
Discard for a Charm effect. Seems about right at $5. You could buy this with some in hand to drain e.g. Duchies, but that tends to not be a concern with Charm itself. Nice card. Not flashy, but not every card needs to be.
Contender
Locked Treasure - Treasure-Liaison, $4
You may spend a Favor for +1 Buy, +$3.
Setup:Choose an Action Supply pile. When you play a card from that pile, first get +1 Favor.
Makes a pile a Liaison! Uh, this feels a bit too good? If the pile is weak or has cards that are hard to play (e.g. Search) this seems fine, but if this hits something like the Village of the board, then this is just a Gold with +Buy, which certainly is good at $4. I do like the dynamic of spend the Favors or get the money here, but it seems like you'd unlock the Treasure too many times over using the Favors. Try this at $5, I think it'd be alright there. Good card, though!
Contender
Mining Company - Action, $5
+4 Cards, +1 Buy
The first card you buy this turn must be a Treasure.
Man, I like this, but it compares too favorably to Council Room. Council Room's downside of allowing your opponents to draw a card does have counterplay, but it importantly is stackable so that there's a downside to playing too many CRs. Contrarily, no matter how many Mining Companies you play each turn, you only have to buy 1 treasure to trigger its effect. This is just too powerful, unfortunately.
Annuit Cœptis/The Eye - Event, $0; Artifact
Take the Eye and put a Token on it. Gain a card costing $1 per Token on the Eye.
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You can't buy Annuit Cœptis.
Setup: Put 3 Tokens on here.
Other people have made better commentary than I could on this Event. tl;dr: Either this doesn't get touched because there's too much benefit from letting your opponent buy it, this gets bought a couple times and unfairly biases one player, or both players use this to drain the Provinces. In all cases, this isn't healthy design for a card. Sorry. This looks cool, but absolutely doesn't play well.
Taxidermy - Project, $3
Once per turn: During your Action phase, you may spend an Action for +1 Card.
Feels similar to Dog Breeders, submitted before this, but there's a good bit of distinction here. For one, this is limited to once per turn, where Dog Breeders can be done as many times as you want given you have a Champion or something. This also costs money and can be opened with, whereas Dog Breeders you can just do turn 1. Already talked about the spend-Actions-for-draw thing that Dog Breeders did, so I'm not gonna repeat myself and just say that this is good.
Contender
Honorable Mentions: Dog Breeders, Shady Market, Royal Forest, Locked Treasure, Taxidermy
Runner-Up: Smithy Village/Goldsmith
Winner: Night Market
Congrats to anordinaryman on the win, and thank you to all who entered!