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.
It also has a local API