How does the Passwords app really work?

There is always a trade-off between security and convenience/usability.
If you want to avoid such situations (and are willing to bear the inconvenience), you can enable the use of Touch ID for auto-filling passwords (my default), or completely disable the auto-filling for passwords.

The touch-id option is under:
Settings → Touch-ID & Password → Use Touch ID for auto-filling passwords.

Disable auto-filling for passwords completely is under
Settings → Autofill & Passwords → Autofill Passwords and Passkeys

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