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As it is an Engine related problem, did you considered using other engine for the game? As I know Unreal Engine 4&5 suppots HTML5, also you can easily port to other Target Platforms. The Paper2D system is very good, Also supports 2D lighting with Normal Maps and the Blueprint system makes everything a piece of cake.

(+1)

I will probably wait until HTML is stable and keep developing the game in Godot 4. Will focus on getting Windows and macOS builds out which run way better anyways. Eventually mobile builds aswell.

Sounds good. Anyway, if you change your mind feel free to contact me. I worked both 3D  and 2D games in Unreal Engine, but I think after Godot it could be easy for you.