It's a bit non-obvious that the 1Password iPad app can be installed and used on Vision Pro. After installation, it shows up under compatible apps.
After you launch the 1Password app the first time and log in with your account you'll want to configure Vision Pro to use the app.
Navigate to Settings > Passwords > Password Options. From there, select "Use passwords and passkeys from: 1Password" and "Set Up Verification Codes Using: 1Password."
Going forward, Vision Pro should use 1Password when you attempt to sign in or create new accounts.