The facts how the local baron sussed out who she actually was:
A clearly educated and relatively affluent unmarried young lady opens up shop in his town.
She is clearly unfazed by beastmen, quite opposed to what the usual reaction to beastmen is.
The local baron would have heard of her, or his wife would have, or the servants , or... After all, she is quite outrageous. So is, in fact, her "humble shop".
Then... During an unprecedented attack on the town, there is a sudden outbreak of Magic. Of a sufficient scale that it screams "Noble". And the only really significant newcomer in town is that outrageous young lady running that coffeeshop those beastmen like to hang out at.
Put A to B , and the Baron goes to have a Look-See for himself to figure out what the hell he is dealing with in his town.
....And he immediately recognises her for who she is...
And not because he is clairvoyant or is that "in" on current affairs.
Our lovely protagonist was engaged to the damn crown prince of the nation, and was so for years. Her qualities, including the nature and strength of her magic, would be very well known to all nobles. It's crucial for them to know. She was slated to be their and their children's Queen. Not exactly a minor matter...
He might not know exactly what she looks like, but he damn well can take a damn good stab on pinpointing her actual identity.
It's not that hard to link the disappearance of a major noble lady from the Court Scene, and the appearance of a magic-wielding ( the paperwork was a damned good subtle trick to test her...) young lady "running a humble coffeeshop" in his town at about the same time .
Doesn't mean her secret is "compromised". If it ever was a secret to the baron to begin with. Grandpa has clout, and he wants to see his granddaughter safe. And the baron seems to be an intelligent and sensible man capable of Keeping Up Appearances.
My bet is that he'll actually play a crucial role in keeping Brother-dear in the dark in the future.