Pre-Brexit student permit to work permit

I'm finally graduating within the next few months! 😁 Does anyone have experience or know the process of going from a UK national's pre-Brexit student B permit to a work B permit?

My current permit has acquired EU rights ("Gemäss Abkommen CH-UK vom 25. Februar 2019"), so I use EU forms from SEM, pay EU fees, and no financial support proof is required, which gives me hope it should be rather straightforward, as if I were EU.

I presume I apply for a work permit like an EU person at the kreisburo with a work contract? Or do I need the company to apply on my behalf like a 3rd country national, but am guaranteed acceptance due to acquired EU rights?

I contacted the kreisburo, but it didn't give me straight answers, more like see how it goes when it's time - which has me rather worried!