I tried your procedure, but without success. I have 26,314 photos in 1,037 albums and it was easier to navigate the albums when I had them organized in folders nested 3 levels deep. The help for Photos in Catalina still shows that you can create nested folders with albums in them, but makes no mention of sharing the folders with Apple TV.
I noticed that the Apple TV Photo Cache folder inside the Photos Library on my Mac was recreated the first time I tried to view photos on the ATV. The Apple TV Photo Database file inside the Apple TV Photo Cache folder is modified whenever I make a successful choice to share an album with Apple TV.
It looks like your Apple TV is an HD version. I have a 4K Apple TV, so maybe the difference in Apple TV versions makes a difference with this issue.
Selecting an album in the top level of My Albums works, but selecting an album inside a folder under My Albums still fails for me. The funny thing is that the folder appears on the ATV, but without any albums inside. It looks like Apple tried to allow folders in the Home Sharing for photos on ATV, which would make browsing easier. Very frustrating for me.