[clangd] Populate the parse options to CodeCompletion/SignatureHelp.

Summary: A followup of D79938.

Reviewers: sammccall

Subscribers: ilya-biryukov, MaskRay, jkorous, arphaman, kadircet, usaxena95, cfe-commits

Tags: #clang

Differential Revision: https://reviews.llvm.org/D81066