[flang] More clean-up of CookedSource API

The std::string holding the content of a CookedSource no longer
needs to be exposed in its API after the recent work that allows
the parsing context to hold multiple instances of a CookedSource.
So clean the API.  These changes were extracted from some work in
progress that was made easier by the API changes.

Differential Revision: https://reviews.llvm.org/D87635