[lldb][test] Rewrite TestStringPrinter.py in a non-inline API test style (#174385)

Motivation here is that I'm planning to add more test cases to this and
it's easier to read/maintain as an API test.

Drive-by:
* I also removed the `std::string` checks since those belong in the STL
formatter tests.
GitOrigin-RevId: 3c32360c83b98850733801f45dd6cef472fda6cf
3 files changed