I have a residency permit aka a Bleue Karte - which is tied to my employer. I have to maintain a job and it has to pay above 50k euros but it’s good for 5 years.

I don't think German Blue Cards are tied to a specific employer. As far as I know you only have to let the authority know if you change jobs less than a year after getting the card, and beyond that you just need to make above the money limit and you can work anywhere.

I had to when I changed jobs change it into the name of my new employer. But that was probably because I changed jobs before a year.