Can’t sign into iTunes
When I try to sign into iTunes I only have an option to enter my password
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You don't say on what hardware you are doing this. It may be taking the hardware Apple ID as the default ID and only needs the password.
"When you sign in with your Apple ID on your iPhone, you will be signed in to the iTunes Store, App Store, and Apple Music automatically so that you can make purchases or begin using Apple Music quickly and easily."
From: Apple ID & Privacy - https://support.apple.com/HT208650