Home Sharing on your TV requires the Apple TV box. Do you have that? If so, which model?
Identify your Apple TV model - Apple Support
Find your Apple TV model number - Apple Support
Home Sharing is not available for third party devices with the Apple TV app.
Apple TV app vs. Apple TV box - Apple Community
Home Sharing to the Apple TV box requires that the sharing Mac has the same Apple Account set for Home Sharing as that the Apple TV box has set for Home Sharing. It won’t connect if those don’t match.
On modern Macs (with the TV app instead of iTunes) (macOS 10.15 or later), you can set the Apple Account for Home Sharing in System Settings.
- System Settings﹥General﹥Sharing﹥Media Sharing﹥
﹥ⓘ﹥☑ Home Sharing﹥[enter Apple Account].
On the modern Apple TV box, you can set the Apple Account for Home Sharing in Settings.
- Settings﹥Users and Accounts﹥Home Sharing﹥[enter Apple Account]
A support guide from Apple: Use Home Sharing to share media from a computer to other devices - Apple Support