Another problem is that when you are building up all of those tabs you are setting up a lot of context in your mind, returning to that context is going to be jarring or impossible. Maybe a replay feature (to show how you created that session, link-by-link) would be a nice idea: "remind me what I was doing."

That sounds like browser history.

To make it crystal clear:

Lets say you have 7 tabs open. Your browser history may include many more websites than were present in those 7 tabs: websites that you skimmed, rejected and immediately closed during your research, or websites you visited while slacking off. The history also doesn't describe how you reached those 7 tabs - it describes everything you have seen. 2 of them could be search results, 5 of them could be pages opened from the search results, and 2 of those 5 could be navigations done without opening new tabs. There may be 20 or so tabs that you opened that are now closed. It is not straightforward at all to manually derive that information from a simple list of sites that you saw. The replay would consist of seeing yourself navigate to that current state (ignoring all the abandoned paths a.k.a. closed tabs) - screenshots with the links you used highlighted as an uninspired example.

Live action replay might have been more appropriate.

If I understand correctly the bookmark was an URL + the Cookies related to it?

Importantly (to me anyway), you can have multiple tabs to the same site open at once, each with a different session. Tabs opened from one of those tabs will retain that session, so you can e.g. fire up two Google accounts, open a few YouTube tabs from each, and keep your viewing history separate. It's like Chrome profiles on steroids, with way less memory use, and way easier to use.

I wander how was the UX, when would you decide to create a new "session"?

So, I'd probably recommend trying it yourself too (really, it's a nice alternative browser. many are horrible, this one I used happily for quite a while), but you can only really trigger the behavior by starting a "single-session tab" which is cmd-shift-T instead of cmd-T. Single-session tabs are basically the same as a "private" window, but if you save a bookmark, you save the session.

This is all reinforced by having the bookmarks bar (on the left) primarily populated by dragging tab favicons. It feels like you're literally saving the tab for later, and it behaves exactly like that, unlike normal bookmarks which use whatever global session state you currently have. In Stainless, the bookmark will always bring you to the same page. Elsewhere, a bookmark will take you to the page only if your current user can see it, possibly showing an error, making you log out of your current account....

Honestly, this is one of the few real new-things I've seen in bookmarks/browsing, and I really grew to like it. It's a far nicer experience.