The big change for me has been realizing that all my "tabs" are still there, in the form of my browser history, or if not, via Google search. If I can't find my way back to a website via my history or via searching the web, then I probably also wouldn't be able to find it among 1000 tabs. So why not close the tabs and be free of them?
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.
The only reliable way that I've come across for finding stuff after a long time has passed is saving every sightly interesting webpage to Zotero and using fulltext search afterwards (including webpage body).
I'm curious, do you find the builtin browser history facilities sufficient for your needs, or are you using some third party tool for that?
Mostly though I realize I have focused heavily on not having clutter vs. being able to recall quickly everything I've ever found necessary or useful. It's a trade off I like, but it may not be for everyone.
I find that browser windows are much easier to manage than tabs and make it possible to see more than one site at a time as well as have different sites/pages sized differently. If I'm doing heavy web research, I'll typically have many browser instances, each with three or four tabs.
I mentioned this below, but check to see what your history limits are in Firefox (https://support.mozilla.org/en-US/questions/1039372). It's possible if you do enough browsing that you might have trouble finding older pages because they're not there anymore.
I'm not sure what the best mitigation is for that, I've kind of accepted that history for Firefox is short-term, not long-term. It might be possible to rig up a webextension to save history more permanently, but I suspect it would need to do native messaging I think to do that, and at that point maybe it's better to just do regular copies of the SQLite database.
Relying on Firefox history less also has the kind of minor advantage of allowing you to be more aggressive about cleaning it yourself, which can have a noticeable performance impact in some cases.