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

[Krystian Stasiowski via cfe-commits]

sdkrystian wrote:

@mschessler Unless @erichkeane, @zyn0217, or @mizvekov object, I think we should merge the original embodiment of my reapplication of the patch. 

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