[clang] Introduce `SemaCodeCompletion` (#92311)

This patch continues previous efforts to split `Sema` up, this time
covering code completion.
Context can be found in #84184.
Dropping `Code` prefix from function names in `SemaCodeCompletion` would
make sense, but I think this PR has enough changes already.
As usual, formatting changes are done as a separate commit. Hopefully
this helps with the review.