Yeah, the extension doesn’t work very well on mobile. There’s a new feature in the app that allows you to group tabs. If there’s an API for it, the groups could be treated as “windows.” Other than that, another solution would be to treat all tabs as a single “window.”

I didn’t quite understand what you meant by “sleep mode”. Consider opening an issue on GitHub.

https://github.com/mateus2k2/tabkeeper/issues