Firefox also has a "always use private browsing" option that I've been using for about ~6 months with great success—with a password manager the only annoying thing to do is get through sms "2fa" gated auth—mostly banks, health insurance, etc.
Always private browsing as a default is a very good idea. I set Safari for auto-privacy. The overhead of manually opening a non-private browser when that is what I want is really a very small hassle.
Setting up Safari this way and using FireFox only with containers for each major web platform works really well for me and I have been able to talk non tech friends into trying it.
