Sometimes I get the feeling that even my own country (Portugal), with all its issues regarding work conditions, still appears to be in better shape.
I am no lawyer, but I don't expect that under EU work law anything done outside work can be forbidden in the work contract, in any member country.
The only issue I see from law point of view, is if whatever is being done, in terms of private projects, is related to knowledge acquired during the work activities, sometimes under NDA. Here yes, there can be issues.
Now if the projects are done in technology stacks or business domains completely different from what happens at work, then it isn't enforceable.
However I am no lawyer.