Is this addition related to making Receiver<Initialized>::process_response consume self? It seems to just be used in the integration test.

yes. Integrations may also need to use this depending on how they are polling.
Pj-cli for example doesnt call this but uses a match

match state_transition {
                Ok(OptionalTransitionOutcome::Progress(next_state)) => {
                    println!("Got a request from the sender. Responding with a Payjoin proposal.");
                    return Ok(next_state);
                }
                Ok(OptionalTransitionOutcome::Stasis(current_state)) => {
                    session = current_state;
                    continue;
                }
                Err(e) => return Err(e.into()),
            }

In most cases I imagine a match would be cleaner.

Edit: I could update the integration tests to also use a match. I figured it would reduce boilerplate. Lmk

I see, since the Receiver is consumed callers need a way to get it back. I'm wary of adding helper methods to the public API just to reduce boilerplate unless there's a clear need. I agree matching seems more correct in general so I'd consider deleting all of these helper methods on OptionalTransitionOutcome or making them pub(crate).

Replaced with a if let clause

                let mut session =
                    if let OptionalTransitionOutcome::Stasis(current_state) = response_body {
                        current_state
                    } else {
                        panic!("Should still be in initialized state")
                    };