[clang] Refactor: Introduce a new LifetimeKind for the assignment case, NFC (#99005)
The current implementation for the assignment case uses a combination of
the `LK_Extended` lifetime kind and the validity of `AEntity`, which is
somewhat messy and doesn't align well with the intended mental model.
This patch introduces a dedicated lifetime kind to handle the assignment
case, simplifying the implementation and improving clarity.