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

[Martin Storsjö via cfe-commits]

mstorsjo wrote:

This no longer reverts cleanly - 4336f00f2156970cc0af2816331387a0a4039317 (#110387) interferes; can someone more involved in this take it upon themselves to sort this out (revert back to green again)? I can of course revert both too.

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