> Does it mean that even people who reside outside jurisdictions touched by the age verification craze will have to deal with all this?

Yes, it's global

> If the estimator falsely declares someone an adult, is Discord legally liable?

Not until a court case on the topic gives us precedent.

On-device doesn't have to mean on "your" device - they might refer to smartphones with remote attestation (like AVF pKVM) which of course are not really controlled by you..