If you're okay with using chrome: create another profile and only use it for jenkins, in fact, set up a shortcut that opens it in app/kiosk mode and maybe see if there's a commandline flag to clear all history every time you open it, that way all you need to do is click the shortcut and everything else happens in the background and it doesn't affect the rest of your browsing exp.
If you're okay with using chrome: create another profile and only use it for jenkins, in fact, set up a shortcut that opens it in app/kiosk mode and maybe see if there's a commandline flag to clear all history every time you open it, that way all you need to do is click the shortcut and everything else happens in the background and it doesn't affect the rest of your browsing exp.