I got similar problem to Update Android TV app, scoped storage problems , where syncthing won’t let me browse or select the folder to sync, giving the error “You do not have an app that can do this”.
This is on Google TV Chromecast running on android 12, and syncthing-fork installed from F-droid. I understand this problem is related to google having removed the “build-in android file picker” from android TV.
I installed many file managers, but none solved the issue. Eventually, I realized that if pressing on the gear icon next to directory option (when adding a new folder to sync on syncthing )in syncthing with the Google TV remote, rather than using the mouse, it worked, and it allowed me to browse and select a folder to sync.
In short: use the google tv remote instead of a mouse to select the directory of the folder to sync.
