In case we want to change this again in the future, I wonder if we should stop having this be a pub field, and instead have a take_unsolicited() method, or something like it? Maybe:

impl Session {
    pub fn next_unsolicited(&mut self) -> Option<UnsolicitedResponse>;
    pub fn all_unsolicited(&mut self) -> Vec<UnsolicitedResponse>;
}

That way the exact type we use here isn't exposed in the API, and thus can be changed. What do you think?

Maybe even:

    pub fn all_unsolicited(&mut self) -> impl Iterator<Item = UnsolicitedResponse> {
        std::mem::take(&mut self.unsolicited_responses).into_iter()
    }

Moving out of the field safes us an additional allocation of a Vec, while still hiding the concrete queue-type from the public interface.

That works too, though maybe -> impl ExactSizeIterator to be even nicer to the caller :)

I think this should be a push_back, no?