I also came to this group, to ask for pretty close to the same thing.
I am actually wanting to find an easy way inside of Session Buddy to either move tabs, preferably more than one, from one window to another.
Or, what I really want, is to take tabs that are in common and save just those tabs as a session. That would be really helpful.
But if I could also transfer them all to one window, either an existing or a new window, that would be fantastic.
For example, when you do a search using any keyword, perhaps part of or all of a domain name maybe, and then let's say you find a handful of tabs for that domain or subject, or whatever one might call it, but you want them altogether, so there not in several windows or you want to just save only those tabs, as a single session... either way would be really, really useful.
I happen to use Vivaldi, which allows me to hibernate tabs. But I'm a tab-a-holic, that loves to keep the history that leads up to any particular place that I end up within a tab. That also allows me I have tons of tabs open, with only a handful of them out of hibernation, because my list of tabs grows, then I just hibernate them so they take up far less resources.
This extension is absolutely awesome, helps me figure out what tabs are actually already open, in any window, without needing to take lots of time to hunt it down, plus, it allows me to find and then terminate tabs I don't need, like duplicate tabs, that somehow are opened in more than one window, and then better use the ones I have already open ready to go.
I just wish I could save special sessions and better move tabs around. I'm working on whittling down the tabs I have open, but it's a slow process.