Nah, it won't because it happens all the time that my password manager doesn't recognize the current url because the auth signin flow had so many weird urls in it that I had to save the url manually and now it's not the right url so I copy out the password manually instead of autofilling it. This was actually the case for my Google account which I created through gmail but then my gmail password wasn't using the right url for all the other google services. Now that I think about it, this was also the case for my Microsoft account that I got a long time ago through hotmail.
I think that this is a fairly legitimate attack vector and it's sad because I really want to be able to hide the url bar in my PWAs through custom styling to make it look more like a real native app.
Using a browser-integrated password manager or passkey will usually prevent this attack, though.