If you are willing to set up a WEBDAV server on your Mac, you can try AuthPass, which is FOSS project that uses KeePass password database.
You don't have to expose your WEBDAV server over the internet if your iOS device is in the local network with your Mac.
Try Authpass. In my experience, it has been really good (but has some autofill issues on mobile(none for iPhone, slightly buggy on Android) and they just added cloud sync (but only for the authpass app).
I recommend giving AuthPass a try (https://authpass.app/) . I switched to it after finding the semi-open-source situations of other products weird and their fee models a bit shocking: AuthPass accepts contributions and I have paid and will keep paying. The UI is going to be very different than what you are used to but I was able to adapt. The author is very responsive and professional as well.