This was the actual problem. Most of ES extensions are not available in
WebGL, thus the GL headers and the code was far more bloated than it
needed to be. The GL header is now reduced and the previous 13 commits
were disabling features that aren't actually available in WebGL.
The final executable size is reduced by ~50 kB, which actually isn't
much, but still something.
Some ES extensions (ANGLE_depth_texture and ANGLE_instanced_arrays) have
now WEBGL_* prefix. I'm still using the original prefix in the
implementation because there are headers for these, but in public docs
and elsewhere they are exposed with WEBGL_*.