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

[Krystian Stasiowski via cfe-commits]

sdkrystian wrote:

Reduced to:
```cpp
template<int I>
struct A
{
    template<int J>
    static constexpr int f();
};

template<>
template<int J>
constexpr int A<0>::f()
{
    return A<1>::f<J>();
}

template<>
template<int J>
constexpr int A<1>::f()
{
    return J;
}

static_assert(A<0>::f<2>() == 2); // error: static assertion failed due to requirement 'A<0>::f() == 2'
```

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