The API is implemented in javascript, and generates C functions that can
be called from godot.
This allows much cleaner code replacing all `EM_ASM` calls in our C++
code with plain C function calls.
This also gets rid of few hacks and comes with few optimizations (e.g.
custom cursor shapes should be much faster now).
Which means that reduz' beloved style which we all became used to
will now be changed automatically to remove the first empty line.
This makes us lean closer to 1TBS (the one true brace style) instead
of hybridating it with some Allman-inspired spacing.
There's still the case of braces around single-statement blocks that
needs to be addressed (but clang-format can't help with that, but
clang-tidy may if we agree about it).
Part of #33027.
