But there's no jurisdictional reality that any of country/union A's rights will protect a person while they are present in country/union B.
In the same way that a US citizen does not have legal protection for free speech when present in, e.g. China, Saudi Arabia, or Germany.
Even if the EU got the text incorporated into the UN Universal Declaration of Human Rights, there are famously many countries who are not signatories (and it would require a locally-implemented actual law to support its recognition).
The EU can arrange post facto penalties for violations of their citizens' rights, to be (potentially) administered in the future, when a responsible entity enters EU jurisdiction, but absolutely not before then without cooperation by treaty with the nation where these foreign-and-not-real "rights" were violated. Which would be a surrender of sovereignty and basically unimaginable.
(No comment on the goodness or successfulness of the GDPR here, just that no part of it is relevant outside of the EU regardless of how the text is composed.)
(And this is all written with awareness that the US somehow manages to selectively enforce their laws extra-jurisdictionally in weak foreign nations. The EU is not the US, and the US is not weak.)