https://addons.mozilla.org/en-US/firefox/addon/tabs-aside/ looks like could be a candidate for you. But I don't know if it closes the tabs automatically after creating bookmarks. From the terminology "aside" I would assume its "move" operation. I never used this program and cannot say how trustworthy or good it is and only post it here based on the description.
It looks good, but last time I tried it, it seemed to make heavy use of the tab hiding function, which really bothers me for some reason.
They seem to have added a lot of stuff, I'll give it another try ! Thanks for the suggestion.
No you can only copy a tab to bookmark, not move it.
It feels the same as "copy then close" when you only handle dozens of tabs, but I handle multiple hundreds and it just doesn't work great, often the saving tab stops midway without notice.
I need a real "move tab to bookmark" function that works seamlessly, is resilient and doesn't lose tabs.