Thank you for your feedback!
I have used the "Asynchronous shader compilation", which was introduced in Godot 3.5. It eliminates the stutter. Without this it was stuttering whenever something new happened (so mostly in the first minute of the game), but the loading time was faster. If you would like to read about the async shader:
https://godotengine.org/article/godot-3-5-cant-stop-wont-stop
It's very easy to change in project settings.
I've also changed "Max Simultaneous Compiles.web" to 4 and "Shader Cache Size (MB).web" to 512. All under GLES 3 settings. I had some issues with the default settings of these two. Everything else is either set to default or shouldn't matter when it comes to stuttering. You might want to try that.
Edit. Be careful with "trimesh colision sibling" as a collision shape. I recently made a mistake and addded only few of them - they were touching each other. It absolutely destroyed performance on the html version and had no impact on the .exe version. Changed them to "single convex" collisions to eliminate the problem.
