Maybe through Academy. Palatine will say later that Ariel was well known for her intelligency and beauty so there were legends of her even after her graduation. And when talking to Jean, Ariel said that her motto (loyalty to Joachim but not to the people in power) was inspired by someone who she respects greatly. I guess she talked about Maximilian.
this is a theory but spoiler just in case
I'm sure people have pointed out the possibility of max and baden working together and I believe max is being considerate of jeans feelings because he's yk planning his own downfall as he believes is the right course of the kingdom which he states in that specific letter and he doesn't want him to be overly attached to him as little pearl especially knowing how much he means to him already so he'd know he'd be in shambles if anything happened to his little pearl. of course there is also the practical aspect where baden who is already anti aristocrat in this gets her share of the deal by contributing to the protest. thinking about it wouldn't it be advantageous for both sides if thought like this?
I already know that Maximilian is little perle but can someone spoil why Ariel is pretending to be him?