in Apple TV menu, just get "Photos" when I click on "Computer", what is wrong?

What is your model Apple TV? Identify your Apple TV model - Apple Support

Possibly you are accessing a library from a networked computer that doesn’t share anything else but photos? Categories with no items to share will be hidden.

What kind of computer are you trying to home share from? What is its version OS?

Use Home Sharing to share media from a computer to other devices - Apple Support

In Monterey, home sharing photos can be set in System Preferences﹥Sharing﹥…

In Monterey, home sharing videos can be set in the TV app. Any video compatible with Apple TV (3rd generation) that has been added to the library will be shared. Note that the Mac will support formats that your Apple TV may not.

In Monterey, home sharing music can be set in the Music app. Any music compatible with Apple TV (3rd generation) that has been added to the library will be shared. Notably tracks from the Apple Music subscription service are not compatible with Apple TV (3rd generation).

Apple TV (3rd generation) technical specifications - Apple Support

↳ Video Formats

I cannot find any menu for home sharing, neither in the TV app, nor in the Music app.

The Home Sharing settings are in System Preferences, not in the various apps. Like the on|off setting.

The Library of the TV app and the Library of the Music app will be shared, when active. That is where you add content.

Sharing is now its own background process. The TV app or Music app do not need to be active when accessing shared content.