I am using a similar extension Session Sync, but it exists only for Firefox and has an ability to sync sessions. It just saves sessions as bookmark folders, and sync is done natively by Firefox Account Sync. Despite the last update was in 2019, it still works pretty well.

As I can see from changelog, sessionic also supports sync [3]. It would be nice if it is added to description/readme.

[1] https://github.com/ReDEnergy/SessionSync

[2] https://addons.mozilla.org/en-US/firefox/addon/session-sync/

[3] https://github.com/navorite/sessionic/blob/main/CHANGELOG.md...