Honestly who cares about a manager job title?

Nowadays the titles are so inflated that every man and his donkey is also a manager or director. Many fresh deg grads go in public sector straight away manager and have a big team of dip/o level officers under him, I doubt anyone in the market see them as hot leaders "up to the job of a manager".

Doing appraisal for 2 people doesn't mean anything, it's the complexity of the role, your current salary (clearest indicator of real rank) and company brand you work with that is the most important in what future employers look for.

There is really no choice for you and any response is solely for show as she already tell you she doesn't care. So either quit or just suck thumb and carry on.

Personally I would just wait and see how the situation unfold. No need to make hasty conclusion too early. Sometimes new boss just want to wayang to show their authority and scare their subordinates to not try stunt.