I use Bookmark OS, have a recipes folder, and use tags for cuisine type. There's icon previews and sorting that I fine super useful. It works super well for desktop and is mobile optimized if you need mobile access. Highly recommend :) https://bookmarkos.com
You could try exporting the bookmarks to an HTML file as that will work in pretty much any browser to import. Also there are likely to be potential issues moving the bookmarks directly.
I would consider a site like Bookmark OS (https://bookmarkos.com/) where you can import your bookmarks and then you can access that from any browser. And it includes extensions which make using it very easy though I find just having a pinned tab works well too.
If you're interested in this thread, you might also enjoy
https://bookmarkos.com/ and https://bookmarkos.com/every-bookmark-manager-ever-made.
"...an attempt to categorize every bookmark manager ever made into the following categories: visual-based, list-based, start pages, search-based, tag-based, tab management, read it later, image bookmarking, privacy-focused, sync-based, offline downloadable solutions, and other."
Caveat: last updated 18 June 2021.
You can use about:support and look for the Profile directory. You can copy the contents to a new profile in Firefox after using the said profile once. In that way you can restore all your settings. If in Classic, you can also use FEBE (http://softwarebychuck.com/febe/febe.html) to make a backup of all your data and profile and once FEBE is installed you can use it to restore the whole profile or just specific data like bookmarks. Another method would be to upload your bookmarks to https://bookmarkos.com and use it moving forward so your bookmarks are available to any browser you happen to be using.
While not a solution have you considered uploading you bookmarks to a service like Bookmark OS (https://bookmarkos.com/) and accessing and controlling them there? When Xmarks closed down and I could no longer sync my bookmarks easily between browsers I ended up using this service. You can import your HTML backup. They also have extensions to make it easy to use though I just keep my bookmarks open in a pinned tab. That way no matter what browser or device you use your bookmarks are always ready to access. BTW this is free if you don't go over a certain amount of bookmarks.
Inside Waterfox you can go to Bookmarks menu > Show All Bookmarks > Import and Backup > Export Bookmarks to HTML and then import the bookmarks into Opera. Not much else can come in directly. Another option would be to use that HTML file to put them in a site like Bookmark OS (https://bookmarkos.com/). Then you can access them from any browser and there are extensions to make access easy. The free version doesn't allow easy nesting of bookmarks in folders but if you used a folder structure on the bookmarks exported you can add new bookmarks into that structure.
Unfortunately, none of the answers so far were able to help me, but I did stumble upon an interesting site in the meantime, which catalogs a lot of bookmarking programs:
https://bookmarkos.com/every-bookmark-manager-ever-made/
Of particular interest to me was the "Offline downloadable solutions" section, and among them, I gave Zotero a try. It has some kinks here and there (importing the exported bookmarks from Brave didn't work well), but it has a lot of useful features like a Chrome extension connector (so it saves bookmarks to the program from your browser) and duplicate detection.
I'm gonna give this one a try for a while and see if it is worth using.
I recommend checking out Bookmark OS - you can make folders for each of your classes. In these folders I have notes folders with individual date stamped notes. And then I keep class bookmarks and to-dos in each class folder as well. https://bookmarkos.com
Instructions on exporting your bookmarks here: https://bookmarkos.com/ultimate-chrome-bookmarks-guide. It will save to an HTML file which you can then import into the new Chrome.
I use BookmarkOS.com. I use a Mac, Windows, and iPhone/iPad. It works very well for organizing my bookmarks into folders and supports tags. They provide bookmarklets as well as browser extensions. Costs me $12/year. They have a demo on their website.
If you're looking for an alternative check out Bookmark OS. I moved from Chrome bookmarks over a year ago and it has been working very well. There's things like screenshot icons, time filters, starring, etc... which make it easier to manage my bookmarks
Pocket is probably your best bet and it is definitely very functional without the subscription storage. Depending on your tastes and how you end up using it, I'd also recommend looking into the following:
Raindrop - I think I use this one the most due to it's separate folder features. It also has a subscription service that you don't need - I've used it a couple years even for gathering research articles and haven't needed to get the Pro version - all devices/OS's covered: https://raindrop.io/app/#/install/mac.
Stash - same story here. Workable without the subscription. A little bit of smart bookmarking here as when you use the Chrome or iOS extensions it filters what you save into it's own classifications (e.g., article, song, product, image). https://stash.ai/
BookmarkOS - Not to be repetitive, but same thing. Free and paid versions. Very solid product. You won't feel limited if you don't upgrade: https://bookmarkos.com/
Hope any of those help. Enjoy!