[docs] try again to handle doxygen everywhere (#203081)

The previous attempt at this (b7da9565017e32c18b927a7637714d1b660b558d)
still broke standalone builds. Now I have locally tested standalone
flang, runtimes (with openmp), lldb, combined builds, and the utils
script. Hopefully that covers everything this time, and gets everything
into a more consistent state (always using the HandleDoxygen script in
the same way, included exactly once as required by the cmake design).

GitOrigin-RevId: 7daddf2b6f44960344157a0accb3963a7d87ca03