[CI] Continuously test typings

[kyranet]

Is your feature request related to a problem? Please describe.

It happens sometimes that users don't test typings changes or TSC isn't very useful at times, 745a0ea (in master) turns the build step for all TypeScript bots red, which is annoying (or at least CI does, I can't get the error in local but my VPS does).

Describe the ideal solution

We should add an extra job in GitHub Actions to run TSC over a TypeScript Test Suite, that way we can ensure typings are 100% correct, and furthermore, this should be compatible with --strict.

Describe alternatives you've considered

Making a PR fixing it... but I don't know how the previous way worked...

Additional context

None.