[clang] Reapply "[Clang][Sema] Refactor collection of multi-level template argument lists (#106585, #111173)" (PR #111852)

[Ilya Biryukov via cfe-commits]

ilya-biryukov wrote:

cc @gribozavr because this commit seems to break the nullability analysis (not upstream, but we've had previous discussions about it and have made changes to keep it working)

https://github.com/llvm/llvm-project/pull/111852