I have no clue about the WebGL issue however for the sticking to walls I'm pretty sure you just attach a PhysicsMaterial2D (Friction=0, Bounciness=0) to both the walls and the player characters and they'll work assuming your movement works with that sorta system.
Viewing post in On Your Shoulders jam comments
so yeah, thanks for the hint and i will use your method next time, but i somewhat fixed the problem and added the web design, so could you play this version and make new rating? Or at least play it and tell me about the experience, what you would change etc. https://antyco.itch.io/on-your-shoulders-033-fixed-web-edition