Simplify diagnostic error management for MLIR properties API (NFC) (#67409)

This is a follow-up to 8c2bff1a which lazy-initialized the
diagnostic and removed the need to dynamically abandon() an
InFlightDiagnostic. This further simplifies the code to not needed to
return a reference to an InFlightDiagnostic and instead eagerly emit
errors.

Also use `emitError` as name instead of `getDiag` which seems more
explicit and in-line with the common usage.