I absolutely adore this mechanic, and I want to play a full game of manipulating objects with my mouse while platforming. One tip; lock the platform you're standing on so it can't be moved around, I accidentally "pulled the rug out from underneath me" a few times.
I think the main thing this is missing is just some friction on the ground. Right now it feels like the character is on ice! The way I handled that in Quadropus is really simple: if the player is not holding down a button to indicate they want to move left or right, start applying some friction. Just set up a small export float and reduce the x velocity by this amount whenever the player isn't actively moving.
Once the player has slowed down to or below a minimum speed (set up an export value for this too), you just immediately stop the player - set velocity to Vector2.ZERO.
This gives you two simple export variables, minimum speed and ground friction, that you can tweak to find the perfect amount of grip for your character. To figure out what to set the actual values to, just boot up your game, run around a bit, and without closing the game, just change those export values in the inspector, and you'll see the game update live! You don't even need to restart it! I don't know if you knew this already, I learned about this during this jam myself and it was a revalation! Makes prototyping and tweaking stuff so much fun.
By the way, feel free to poke me on the Discord if you ever wanna chat about player controllers or anything else! I'm @lemonsaurus in there.