I ran into this same issue. Finally took until Christmas break to have the mental space available. Switched to Firefox + Kagi, and very happy that I did.
I wasn't able to quickly find an answer: can you use it also in private browsing mode on Firefox? I basically only use private Firefox browsing both on mobile and desktop.
They give you a unique URL associated with your account that you can use without manually logging in. It does somewhat defeat the purpose of private browsing mode depending on what you're using it for though.