There really isn't one. The closet would be Konqueror with KHTML and one of Mozilla's discarded projects called Servo (which is a beta project now run by the Linux Foundation). The rest are Chrome in a wig and Safari.
EDIT:
I can't remember where I learned this, but I swear someone on lemmy had shown some tweets that were showing support for the musk era changes and were in some way endorsing web3 garbage. Take everything anyone says on the internet with a grain of salt.
There was a comment thread a month ago about the attempted refusal to use gender neutral language because that's political: "This project is not an appropriate arena to advertise your personal politics."
It's not the same thing, but it does match the pattern. Still take everything with some salt though.
I experience little breakage with Librewolf, and when I do, maybe 75-85% of the time it is because the site only works with Chromium. I get extensions directly through the browser, I have not enabled anything as far as I am aware. And of course you can configure the cookie clearing. I quite like it, there are (in my case at least) not many exceptions you need to add before it works quite smoothly, but of course that depends on your usage.
I use plain old firefox there are few sites that require chromium. I have noticed that enhanced tracking protection and adblock can both break some sites. Whether it makes sense to turn them off or use a different site depends on the site.
Is it a true fork, or is it a project that follows the Firefox tree and builds a customized browser from it?
The difference being, if it's a true fork, they have to do all their own browser engineering starting at the time it was forked off. That sounds like a monumental effort.
Doesn't Safari use a different codebase? It's not available on non-Apple platforms, but it's good to know that there are still engineers working on a different codebase.
So really, all modern browsers are either forks of KHTML / KJS or are based on the Mozilla codebase. But, at least right now, there are 3 separate engineering teams working on 3 independent codebases. Which hopefully will mitigate some of the issues you get when one company completely controls a software "ecosystem".
As I notice this comment is satirical, unlike the (currently) 49 plebeian downvoters, I feel my massive genius brain undulating and pressing upon my skull.