After the interview, I asked for a letter of recommendation and gave the message a few days later.

About two weeks.

It depends on the tutor. If it's more than a week, I suggest you send an email to ask if you have received a recommendation letter from an expert. By the way, your ability and work during your doctoral period are in line with the research direction of this tutor, and you are very confident that you can be competent for his work. Finally, express that you really want to go. It's also possible that these ... all treat you as something else. Keep looking for something more suitable. I'll come to you if I can't find it. So we can't stick to one possibility. Looking for a job is not falling in love. You don't need one-on-one I suggest you wait while looking for it. You can't hang yourself from a tree.