want to manage plan but no manage plan button

It looks as if you may have an enterprise (or student/teacher) account. You cannot manage this yourself., and Adobe cannot touch your account if it one of these. You have to contact your local administrator.

Try using a different browser/network, make sure you don't have any script/ad blockers or firewalls interfering(try disabling them) and also allow cookies. You can also contact support for help regarding this.

To contact support, login to your account and navigate to the URL below. Make sure that the browser has cookies enabled, and all script blockers are disabled.
https://helpx.adobe.com/contact.html?rghtup=autoOpen
Type AGENT to avoid bots and talk to a human.
Also, be mindful of answering anyone who sends you a private message. See the following for more information about scammers
https://tinyurl.com/y7cfrr7y
-Manan