Do you still have your purebrowser files/installation somewhere on the device?
Generally speaking (though i do not own a librem laptop myself yet) when switching from one browser to another you can always export your bookmarks from one browser into a file, and then from your new browser select to import bookmarks - select the file and voila. If however the update completely overwrote and deleted the previous browser and associated files,it may be recoverable by methods someone far more savvy than me might be able to guide you through.
If the browser,or its files,are still available. Exporting from the first,importing into the second is how i have always done it.
From what i can find, the update should not have removed your purebrowser files but rather switched to firefox ESR as the default browser. Perhaps you will find useful information at this thread on Reddit?
Update to ESR thread,Reddit
Edit: Possible relevant from the thread in relation to this new update-
Will I be able to import my bookmarks [file]?
If the profile downgrade wouldn’t work, you can copy
places.sqlitefrom your old profile to the new one (note: only do this when Firefox is not running).
edit 2:
Even if your purebrowser has been effectively removed ,the old profile used to store among other things, bookmarks, should absolutely be possible to locate. It may be that you have to manually enter it and copy line by line,link by link,each bookmark and insert into your firefox ESR profile or directly copy link by link into the browser and re-bookmark it that way.