I think in this case the behavior is that the initial generation of the password is random, but subsequently it is, shall we say, "trivially deterministic": it (intentionally) always spits out a cached copy of the initial randomly generated password.

I think security implications here would mostly apply to cases where you wanted to create multiple accounts on the same website within a short period.

Deterministic doesn't mean predictable by an attacker who can't read system memory but consider also that this could be implemented as simply as a cache: store the generated password for that hostname for n minutes and reuse it for autofill when present. There are a number of hokey things web developers do around security and this would seem like a good hedge against, for example, the ones who split the password and confirmation into separate forms or make you login to their related services because they haven't setup SSO properly.

That’s why I mentioned “depending on copy” (or more broadly “UI”).

If I’m clicking a “Generate password” button I expected a new password every time. But here it’s an autocomplete-like dropdown rather than an action. By your definition, such dropdown would show different passwords for different fields, even if the second field is a “confirm password” field.