I feel ya! I just barely got in the main game mechanic as learning Godot at the same time was probably not my best idea. LOL And no worries on the gamepad support, some engines aren't as easy as others. One thing I love about Godot so far is how easy it is to add multiple input controls to it. Unity has it but you have to do a lot more work.
Well, actually we're on the same boat then, because I did the exactly same thing LOL. This was my first game using godot and I was also a Unity dev, and that was not a good idea, as I had to sacrifice sleep to learn the engine while making the game, but at least I already had a previous notion on how the engine works, so things we're a bit easier, still I couldn't finish it but i'm happy with the results and I will probably stick with Godot for some time, as I think Unity has a bit slower workflow at least for me. Also, I didn't add gamepad support because I kind of misunderstanded the rule of the limited controls, but I could've done that easily as Godot has a really intuitive input system to work with! (Actually I'm Course, but I am using the game's artist account cuz he's the one who submitted the game lmao)
Really liking Godot so far. I have a few issues with it as it's missing a few features that I'd like to see and I really don't like the heavy use of Strings for things (at least in GDScript), though it seems they've made this a lot better. Unity has this use of strings but in most cases you can code in such a way so as to not use strings or at least put them all in one spot and do code to check the validity of those strings. But overall I really like how quickly you can prototype and build on things in Godot, takes ages with Unity to do the same simple things.
I'll find out more of what does and doesn't work for me when I port my regular game to Godot 4 from Unity. I still have yet to try the C# in it but I wanted to give they're built in code a chance first. This also probably didn't help me in this Jam. LOL But I am happy I did as I learned a lot about it pretty quickly.