[clang-tidy] Initialize DiagnosticEngine in ExpandModularHeaders

Fix issue preventing suppression of compiler warnings with
-Wno-<warning> under C++20 and above. Add call to
ProcessWarningOptions and propagate DiagnosticOpts more properly.

Fixes: #56709, #61969

Reviewed By: carlosgalvezp

Differential Revision: https://reviews.llvm.org/D156056