"Cyber" as an archetype only comprises of Spells/Traps. (No card that references the archetype deals with monsters, though the name fragment Cyber Harpie Lady sort of, but not really, possesses is the same.)
Worth pointing out that due to her name-change condition, she'd never be valid for any "Cyber" support anyway, as there is never a point where a card can be named "Cyber Harpie Lady".
Why this card is an effect monster. It doesn't have an effect.
It's technically not an effect. (For example, if you hit it with Forbidden Chalice, its name will still be Harpie Lady.) Effect Monsters without effects aren't that rare. Cards like Gate Guardian and Exodia are, too.
It's an effect monster so its card text has meaning. (I guess that reasoning isn't as strong now that archetype conditions like Summoned Skull's are a thing, but that's clearly why.)
This card's name change used to be treated as effect iirc, but condition type effect that cannot be negated.
Now it's just a condition, but they didn't revert this card to vanilla, probably for the sake of "continuity/history". It's for the same reason they slapped the archetype condition on OG Summoned Skull, instead of changing its name into "Summoned Skull Archfiend" for example.
I want to make all the harpie lady's chirp my name!