EU doesn’t have that kind of agency.

Member states have spy agencies, but they also signed treaties to join the EU. Having your spy agency violate international treaties isn’t something most governments allow.

If the company or individual is in a country, expect they can be compelled to hand over everything in their possession by a court order (or it can be siezed).

If the information is stored in a country, expect that the owner of the information can be compelled to hand it over by a court order (or it can be seized).

The EU doesn't have something like the CLOUD Act, so they wouldn't be able to do that.

Well the EU absolutely could do the same thing. If an EU-based company had servers in the US, I would expect the EU could compel them to hand over data despite where the data is stored.

The EU doesn’t do law enforcement. That is a national concern. But a legal request from one country to another may well happen.

I misspoke there, I was meaning Europe and shouldn't have put EU.

Agreed, the union doesn't have any enforcement mechanism I'm aware of that would fit, but any country in Europe could do a similar thing to companies based in their borders.