Vlad, apologies for the lengthy delay. Here's some visuals featuring Tab Group start pages. Note that since I am not a macOS beta tester, the images come from Safari on iPadOS 16.1, however the feature is identical on both platforms. The start pages also sync to iOS.

Here is my "standard" tab group — the base one that doesn't sync to other devices. Note that it has a set of Favorites as well as its own background image.

Here is my Travel tab group showing an areas for Travel Favorites, currently empty. Below this section is the general set of favorites shared by all tab groups. Note the background image of the Travel tab group is unique.

Finally, here is my Work tab group showing unique Work Favorites only available within this tab group. Note the unique background image.

Here is a screenshot of the settings dialog for the Edit button on the tab group start page with options to sync the customized start page across devices, including Tab Group Favorites and Recently Closed Tabs using iCloud.
Just to see how the interface scales, here's the same Work start page from above as synced to my iPhone running iOS 16 beta:

Let me know if you have any additional questions.