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

[Alexander Kornienko via cfe-commits]

alexfh wrote:

We've also found a clang crash and a few new compilation errors after https://github.com/llvm/llvm-project/pull/114569. We definitely need to revert it as well as this commit.

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