HTML5 with GLES3: Game takes a long time to start (spins at 100% CPU utilization)

[gandalf3]

Godot version:
Tested with 3.2.1 stable and latest master (b0eca58).

OS/device including version:
Archlinux
Firefox 76.0.1
Chromium 83.0.4103.61

Issue description:
Loading the exported html in Firefox or Chromium pins one CPU core to 100% on a black screen for around a minute, then the game starts.

No errors are reported in the console, though there are a few webgl warnings that appear after the delay:

WebGL warning: getBufferSubData: Reading from a buffer with usage other than *_READ causes pipeline stalls. Copy through a STREAM_READ buffer. 2 html5_test.js:7:30378
WebGL warning: drawArraysInstanced: Buffer for uniform block is smaller than UNIFORM_BLOCK_DATA_SIZE. html5_test.js:7:247343

This delay is not present in the same project after switching to GLES2.

Steps to reproduce:

1. Export a simple project to HTML5
2. Start a local server (e.g. python -m http.server 8000.
3. Visit the exported html in a browser (e.g. at localhost:8000/html5_test.html).

Minimal reproduction project:

html5_test.tar.gz, just a cube and a camera.

[Calinou]

Duplicate of #21957. To solve this, switch to the GLES2 renderer.