Merge clang-tidy workflow into another existing C++ build

[jhale]

I wanted to get #3722 merged to ensure that the extensive C++ fixes don't become hard to merge.

Nonetheless, the PR introduced a new clang-tidy workflow - could this be potentially be merged into another workflow?

[schnellerhase]

We should run clang-tidy in a build with as many dependencies activated as possible. Therefore the simples choice of the PETSc free, non-matrix build run from ccpp.yml is maybe off the table. Since the compile with activated checking runs quite a bit longer, we don't want to do this in the matrix either.

How about we activate it in the redhat CI?

[garth-wells]

Don't touch the Redhat CI for the moment - I'm in the process of merging Redhat and oneAPI, with Spack + caching. Fewer moving parts and more control.