I don't see how they could legally intervene. Most EU countries have very independent court systems. Once the warrant is sent to the states, it will be enforced.
In EU countries with independent court systems, those EU governments routinely ignore court decisions they don't like. I did a very deep dive into this. There is no European country where checks and balances consistently, properly work.
Surprisingly enough among EU countries, Austria gets relatively close to adherence. Canada is likely the best at it globally (and yes, that takes into account "notwithstanding").