Yeah, sadly once the addon API changed Mozilla removed the possibility to store additional data alongside a bookmark and all the functionality that was based on that (pinned information, and other tab session information) was no longer going to work. I do have a solution in mind to provide this back, but sadly it's not something that can be as reliable as bookmarks and I'm not really sure if on the long run is not worse to implement something that may work only until you delete the addon and then just lose that data suddenly because it was saved in addon storage.

Regarding the "click cancel". Well that's not really what it happens there but I get why you thought that. That dialogue it's actually meant for you to edit the name of the session (which is already saved) so basically clicking cancel will just leave the session with the default name. The same edit box will show if you just go over any other session and edit it's name. I totally missed that it an create confusion if I show the edit box right after saving a session, that's a great observation and I'll think about it if there's anything that ca be done to improve the experience so that saving steps may be more clear. So this is not really a issue... everything works as it should... but I will think about the whole saving process to see if there's anything I can improve to be sure things can get confusing.

I'm not really sure I do understand the 3'rd statement :
"And it would be great if there was an option to manually save session in bookmarks or, like autosave session, in sqlite database in addon data storage folder."
So, saving in bookmarks is manually... or you wanted to say automatically save ?
Regarding addon storage... well that's seems to be problematic since it's not really reliable. Addon storage is there only if you have the addon installed. If by mistake (your or because of Firefox) the addon is removed, add the data associated with that specific addon is deleted right away. For example this is what happenes with the auto-saved sessions, they are simply deleted by Firefox when the addon is removed. So storing anything valuable in addon storage it's not something I can do right now , probably after I add some form of full backup, but even then it seems to me that the addon storage is really good for nothing because it give users the apparent idea that data is save but it's just isn't.

If you have any other feedback you can contact me directly over email (use the Feedback button from the addon menu) or if you have any feature request (or issue) you can also send it to https://github.com/ReDEnergy/SessionSync.

Thanks for detailed feedback (and for using the addon)