Signing into old iTunes accounts fails

I have three iTunes accounts from 2004 until now. The older ones are not legit email addresses (one is just a username, the other is a domain address that Apple assigned) and I cannot sign into the older ones on my iPhone 15. When I sign out of my current iCloud account, attempts to sign into the old accounts on my iPhone 15 result in an endless loop of entering email addresses - password entry - error messages (like Invalid Email, or Cannot Use Recovery Address, or simply just doing nothing). I have music purchased with these old accounts that I want to play on my phone. I can access these old accounts on my iMac. Please advise.