How do I access Apple TV+ on other devices?

Phones and iPads have an Apple TV App. Computers don't. They access Apple TV+ content through a web browser in the same way Netflix, Prime Video, etc. do.

https://tv.apple.com

For Mac:

What is the exact model Mac and its introduction year? Identify the model of your Apple device - Apple Support

What is its version macOS? Find out which macOS your Mac is using - Apple Support

For macOS troubleshooting, try these:

• How to use safe mode on your Mac - Apple Support. ‘Safe mode’ can help you to determine whether an issue is caused by software that loads as your Mac starts up.
• How to test an issue in another user account on your Mac - Apple Support. If an issue stops happening when you log out of your macOS user account and log in with another, the issue could be related to the files or settings in your user account (e.g. preference files).

Let us know the results of these tests.