Safari PWAs currently are not good for this task. Because it doesn’t give access to browser extensions. Which is what you need in this situation. (Unless you want to just use your nsec, which I wouldn’t recommend). 

Nostore browser extension (from the App Store) allows you to sign in using the button “Sign in with extension”. The extension holds the nsec. (Like a hot wallet, sorta speak).

In iOS17.4, Apple is changing PWAs to open like regular windows, which I’m hoping will allow extensions to work properly and fix this mess. 

If you sign in with anything other than the extension or the nsec, you will probably be able to browse your profile only, not interact with it notes. 

Tagging #asknostr for extra support.