Switch to happy-dom for testing (#29948)

Use `happy-dom` again in vitest as it has caught up recently to `jsdom`
in terms of features and it is a much more lightweight solution.

I encountered [one
bug](capricorn86/happy-dom#1342), but it's an
easy workaround until fixed.

I regenerated the lockfile to get rid of the transitive dependencies so
that's why the diff also has some upgrades in it.

In total, this change removes 39 npm dependencies.