Diagnostics: Simplify provider registeration and make it safer

Instead of manual register/unregister calls, rely on RAII. A provider
gets registered on construction and unregistered on destruction.

On unregistering, clear the diagnostics from the provider getting
destroyed to avoid stale pointers in diagnostics.

Also, ensure destructing is fast by clearing everything manually before
disabling plugins.

This fixes a crash after the build plugin merge.