I use Firefox and Brave. It works for me great. I can have one set of tabs open in Firefox and a different set open in Brave. It lets me distinguish between work and private at a glance.
Politics of either do not affect my user experience and unwanted features in Brave can be turned off.
While I have been using Firefox much longer than Brave, some sites don't work in it as well as they do on chromium based browser.
Yesterday I have installed Ubuntu and KDE Plasma. It's a bit of a steep learning curve so far, but I'm open to good Linux based browsers you might suggest.
On Firefox you have profiles (about:profiles) so you can have separate profiles. Also you can use this extension to separate your work accounts and personal accounts in the same profile if you don''t like switching profiles https://addons.mozilla.org/en-US/firefox/addon/multi-account-containers/
If you make a new profile I think on some platforms you will see 2 icons, for me it wasn't the case at first, I tried following this guide for Windows and apply it to Linux, apparently without success, but then I found out that it is KDE's fault for grouping same app windows, so you right click on the icon in the taskbar click "More" and disable "Allow this program to be grouped"