On macOS Sonoma (even all of Catalina and later), users should be able to sign in to the Apple TV app on Mac to watch Apple TV+ content there.
On computers, including the above, users may be able to use browser access to watch Apple TV+ content. Just go to tv.apple.com and sign in there, through the blue Sign In button.
On what model computer and version OS is this happening? Is it this MacBook Air running Sonoma?
What browser (version), if any, are you trying to use to watch Apple TV+ content? Have you tried a different browser?
Verify that you tried to sign in using the email address for the Apple Account to which the Apple TV+ subscription is linked. Signing in with a different email may be a cause of difficulties.
What happens when the log-in fails? Do you get an error message? What does it say?