I'm not sure I follow your workflow exactly. If PR B is merged, then I'd expect PR A to already be merged (I'd normally branch off of A to make B.)

That said, after the squash merge of A and git fetch origin, you want something like git rebase --update-refs --onto origin/main A C (or whatever the tip of the chain of branches is)

The --update-refs will make sure pr B is in the right spot. Of course, you need to (force) push the updated branches. AFAICT the gh command line tool makes this a bit smoother.