[analyzer][NFC] Remove dead code and modernize surroundings

Thanks @kazu for helping me clean these parts in D127799.

I'm leaving the dump methods, along with the unused visitor handlers and
the forwarding methods.

The dead parts actually helped to uncover two bugs, to which I'm going
to post separate patches.

Reviewed By: martong

Differential Revision: https://reviews.llvm.org/D127836