This question has been discussed on and off since 2016 with various approaches. I'd like to define my stated goal, perhaps more specifically than earlier discussions.

I respect the various replies such as:
"We rarely if ever get this request from others";
"Some people have dozens, hundreds, thousands ... of tabs open";

However, suppose, the end-user were limited to certain conditions. Consider the following scenarios:
- There are multiple browser apps (Safari, Chrome, Firefox, etc.)
- A given app may have multiple instances (windows).
- A given instance may have multiple tabs.

EPLICIT BATCH IMPORT:
- Imports ALL TABS from ALL instances of a given browser app.
- The USER must establish a 'clean slate' before beginning a search session.
- Clean out and restart the current browser, OR ...
- Select a different browser app

CURRENT PUBMED WORKFLOW: (** Suggestions Welcome!)

- During a search I open a set of initial target refs (e.g. Ref-A... Ref-J) in individual tabs.
- I may or may not import to Zotero at this point.
- Then, browsing Ref-A I find 'related papers', e.g. A1, A2), which I save as new tabs. Sometimes these are appended to end of the tab list (although descendant from Ref-A); sometimes (?) they are inserted into the existing tab list.
- So is the next tab Ref-B? Or is it Ref-A2? Have I already imported it into Z?

I typically keep the Zotero toolbar open at the bottom of my screen to display refs by Date Added. This allows me to reduce (but not eliminate) importing duplicate copies as I work my way through the remaining tabs.

Sometimes (if I remember), I will detach tab Ref-A to create a new window. Then all descendants are clearly awaiting Z import. However, I have also just created a new instance of the original situation!

PROPOSED WORKFLOW:

A: Start with a CLEAN COPY of BROWSER X.
B: Save initial search results as individual tabs.
C: ** Do NOT import refs as they are discovered/identified/selected).
D: (Optional) As desired or convenient, detach tabs to create new BROWSER X windows.
E: Continue browsing, searching/identifying/selecting related references.
F: Save each descendant reference in a new tab (in any number of new windows).
G: To close the search session, IMPORT ALL TABS.

- NO NEED to keep track of descendants, generations, or family trees.
- No confusion as to which refs have been imported and which have not.
- No duplicate references imported.


Having thought through these various scenarios and clarified my thoughts, I am now thoroughly convinced ...

THIS FEATURE WOULD BE ENORMOUSLY HELPFUL!

Thanks for reading.