It seems that you have trouble accessing Apple TV+ content on the web at tv.apple.com on a computer.
Apple recommends the latest versions of the Chrome browser or Firefox browser for this. Please try one of these, if you used a different one. Watch in a web browser - Apple Support
It is not supported to use TV browsers for such access. These browsers do often not support all the (modern) features that the site tries to make use of.
Sign in to the site through the blue Sign In button in the top-right corner. Once signed in, the icon will change to reflect the signed-in status, and offer a clickable pop-up menu with two options instead: Settings and Sign Out.
If you did all that, and it still doesn’t work, then try deleting website data (cookies) for the apple.com domain. Then try again.