It can be super tricky… when I found my apartment, I didn’t have my dog (Pablo) at the time, and the letting agent had a 100% no pets allowed rule. However what I found was, if the landlord allowed it, and you had written permission, it was fine. Some letting agents can be pretty bad for this, and causes a lot of stress. Worth asking when looking around, and also offering a higher deposit can sometimes help.
Did you see the article on the site? Russell over at Pets Lets might be able to help? https://paaw.house/let-pets-let/