Consider improving warnings.cpp LIT tests

In #3978 I extended the test a bit by adding more explicit template instantiations to get bigger coverage in the test, which actually allowed to find one more warning.

Besides increased coverage, I've also discovered that some warnings are disabled for no (or at least unknown to me) reason and could be enabled back to improve our headers and tests further: https://github.com/intel/llvm/pull/3978#discussion_r656967476

The purpose of this issue is to:
a. increase test coverage by adding more template instantiations to this or other tests
b. review list of enabled and disabled diagnostics to see if we can be more strict, i.e. enable more of them