2 Apple IDs Causing Issues

I’ve had 2 Apple IDs for more than 10 years. My phone requested that I enter my password for 1 of them (I’ll call it Apple 1) in settings. I clicked forgot password and got an email sent to my account to change the password for the Apple ID I was being prompted to provide the password for in my settings (Apple 1) I changed the password and went back to my settings to enter it. When I enter it, I get told the password is wrong, but I changed it and logged in to confirm it. There’s no option to switch the Apple ID to my other Apple ID (or Apple 2). What can I do?