On my mac I can start the TV app but apple tv is not shown in the left panel
The Apple TV app on Mac has navigation options in the sidebar (left panel). It should include “Apple TV+” for accounts set to countries where this specific service is available. It is not intended to show “Apple TV” there.
Apple TV app user guide for Mac - Apple Support
… and account settings does not work (nothing happens when selected)
Account settings can be accessed from menu Account in the menu bar along the top of the screen.
Account settings can be accessed from the account icon at the bottom of the sidebar of the main screen in this app.
Access would quire authentication. You may need to confirm using Touch ID or typing in account credentials.
When I try to authorize the computer, it says I have too many devices authorized, but not how to de-authorize any device.
Users can have up to 5 computers authorized per Apple Account. This count might include previous computers that you no longer have, if you never deauthorized those. Authorization is needed for content downloads; it wouldn’t apply to online streaming, or other functionality of the app. If you need to deauthorize computers that you don’t have access to, then you can deauthorize all, then re-authorize the computers that need it.
Authorize or deauthorize your computer for Apple Account purchases - Apple Support
Mobile devices are counted separately. TVs and streaming devices don’t count for this at all.
Please contact Apple Support if this doesn’t solve it, or if these numbers can’t possibly apply to your situation.