Yeah, I was gonna keep the game a secret (both here and in the devlog), since if I said the name, it would seem like I was pointing fingers or somethin'. Idk. It just felt rude. But since then, they actually gave the public a project file for one of the room and permitted modding for it. So now that there's modding, I've re-recorded part of the devlog to update the outdated info, and now I feel comfortable saying that the game is called garn47, and the engine it uses is Blender. (Yes, the 3D modeling program. It used to have a game engine functionality.)
Glad to hear you're getting into programming! Godot is definitely a good one to start with. Very simplistic, yet powerful! Limbless was actually made with it.
The difficulty of modding really depends on the game and the tools. For example, Minecraft Java, we have tools like MCreator that can make mods near instantly (though it has its limits), or you can code one in plain Java. Of course, Minecraft mods are only this easy because of mod loaders like Forge and Fabric. If Minecraft didn't have these tools, then it wouldn't be as easy, and the modding scene wouldn't be as big. I would give you an example of games that don't have mod tools, but most of the games I play are very moddable. Sometimes moddability is the whole reason I buy a game lol.
Regarding your style question, garn47 itself is already a very weird game, so a weirdcore style is pretty much inevitable. Though, again, I'm not sure if I even will mod it. So if I end up modding something else, then I can't really answer that question, and we'll just have to wait and find out :)