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

[Martin Storsjö via cfe-commits]

mstorsjo wrote:

Thanks @sdkrystian for pushing the revert - now my nightly tests this night were back to green :-)

https://github.com/llvm/llvm-project/pull/111173