Dragging bookmarks probably doesn't work, but you should be able to use Copy/Paste to copy multiple bookmarks from the Library or sidebar to another profile's Library or bookmarks folder. This only works for bookmark, so you can't copy a folder with its content this way (you only get the folder name).

Copying a tab would work via copying the URL to the location bar in another profile or use send to device (Sync).

I paraphrase the answer that addressed the problem and partly solved it. The current Firefox is 94.0.

1. Tabs: dragging and dropping them across different profiles (each open on its own window) is not possible
2. Folders of bookmarks: dragging and dropping them is not possible using either bookmark lists or library views.
3. Bookmarks: it is only possible to drag and drop individual bookmarks or groups of individual bookmarks if the source and target locations are the bookmark lists (Ctrl + B) or library items (Ctrl + Shift + O). This is user-friendly enough when tidying up locally two profiles that have diverged or overlapped against the plans.

The possibility of dragging and dropping folders of bookmarks, together with their content, seems a generalization of transferring bookmarks alone; this is definitely a feature request.

Firefox places various flavors on the clipboard and for place items (bookmarks and history) the preferred format is text/x-moz-place. If you copy a folder then you only get the folder ID to speed up moving a complicated folder structure as that would require to remove and insert all items. Firefox also places text/html on the clipboard and that is the same as used for a bookmarks backup and this is limited to A HREF, but it includes the full folder tree of the selected folder. You can test this by pasting the copied folder in an HTML capable editor. You can possibly use this to backup a specific folder and save this to a bookmarks.html file.

Firefox places various flavors on the clipboard and for place items (bookmarks and history) the preferred format is text/x-moz-place. If you copy a folder then you only get the folder ID to speed up moving a complicated folder structure as that would require to remove and insert all items. Firefox also places text/html on the clipboard and that is the same as used for a bookmarks backup and this is limited to A HREF, but it includes the full folder tree of the selected folder. You can test this by pasting the copied folder in an HTML capable editor. You can possibly use this to backup a specific folder and save this to a bookmarks.html file.

The purpose of dragging and dropping between two profiles (on the same computer) is to work on selections of bookmarks and transfer them locally with agility. Backing up is not relevant here. The suggestion above seems to address only the saving of a folder of bookmarks from a source profile. The missing part is how to add these bookmarks to a target profile without overriding the existing ones.