Does the EU have the equivalent of "feds" in the USA (e.g. DEA) that could catch someone with small amounts of marijuana in the Netherlands and prosecute them not under national law, but under EU law?
Nope. EU doesn't do criminal things. EU tells countries what their criminal systems do. There is Europol (European Police Office) which is only for aiding cooperation between national police forces. It has no powers of arrest, and (most tellingly) it only has 800 staff for a population of half a billion people. Not at all like "the feds".
And I don't think there is any EU law on illegal drugs like that.