So I do have bad news about this that may or may not be news: Firefox cycles history even if you never clear it. Unbelievably it's not permanent.
This has bitten me a couple of times in the past because I always assumed that naturally history wouldn't just get randomly deleted in the background, so I'd search for a tweet or article from an obscure blog and couldn't figure out why nothing was coming up in my history searches. Took me a long time to actually check "is this article I looked up 6 months ago even there anymore?"
There is a way to set up recurring database backups manually if you're willing to do some gruntwork, but it's kind of a pain and means you need to break out an SQLite browser across multiple backups in order to search.
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Where searching is concerned, :shrug: that doesn't generally work for me, but I'm happy for anyone that it does work for :) My tabs aren't just so that I remember where a document is (although they serve that purpose as well), they're also a reminder that the thing exists at all. When it gets to 1000 tabs, is that useful? Arguably no, but the process getting there is pretty organic, it's not really a conscious choice.
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In support of your comment though, being able to just stick all of my tabs in an open text file does genuinely help a lot[0] because it's permanent history and it serves the same purpose of being a reminder. It could be better, sometimes I leave tabs open on images that I forget to get around to saving or on open sessions and then the link rot hits whatever I'm looking at -- but it helps a lot. Being able to have an intermediary step between "leave everything open" and "categorize and organize everything you're looking at and save what you need" does allow me to do things like grab 500 tabs that I haven't checked in weeks and just stick them in a text file and write some notes at the top about what I was working on.
Split browser sessions, better windowing would help a lot with this, although I worry I'd end up with similar situations as my Emacs window, where everything looks clean but behind the scenes I have 1000 open files and 20 of them are unsaved scratch buffers ;) But the text file does kind of work the way you're describing; you can be free of the clutter, but if you really need to find everything, you know it's in a static text file that you can grep through at any time and that you know the browser won't do anything shifty with in the background.
[0]: I say that it's common to have 1000 tabs open, and it is, but currently I only have about 200, largely because of that method. I went through a bunch of stuff a few weeks ago and stashed most of the stuff I had open.