[clang] [analyzer] Turn NodeBuilderContext into a class (PR #84638)

[Diego A. Estrada Rivera via cfe-commits]

diego-est wrote:

I added the appropriate functions and moved the class members into private. Additionally I ran `make check-all` to make sure the now-private members wouldn't cause any issues with the rest of the codebase, all the checks passed.

https://github.com/llvm/llvm-project/pull/84638