[clang-tools-extra] [clang-tidy] check `std::string_view` and custom string-like classes in `readability-string-compare` (PR #88636)

[Piotr Zegar via cfe-commits]

https://github.com/PiotrZSL requested changes to this pull request.

- Missing storeOptions
- Some other tiny nits.
Would be nice to get rid of lambda RegisterForClasses as it's not needed, and have common handling.

https://github.com/llvm/llvm-project/pull/88636