In your opinions what would be more valuable for a hiring prospect to have in business related roles or Porject management roles, a master degree or 2,3 years of work experience?

None of that matters in a vacuum, it's always going to be considered against the rest of the available information about a candidate. What is it you're actually trying to decide here?

I have doubts about if I should pursue my master right after university and have my first full time job after my masters with 24,25 years old or if I should find a job in the game industry right after university.

My biggest concern is about "getting old" without full time job experience, although at the same time some companies like Ubisoft have trainee programs for master students.

what would be more valuable for a hiring prospect

Personally I consider a master's degree the rough equivalent of one year of general experience, plus about six months of experience on whatever specific topic the person researched if they did a thesis, or a combined total of 1.5 years general experience if it was a non-thesis program. This can be valuable if I happen to need that specific skill set at the moment the individual is hired.

I still expect that with only 1.5 years of work experience, both options (the BS+job or BS+MS) will need considerable hand-holding by a more senior developer.

My biggest concern is about "getting old" without full time job experience

Unfounded fear. While there is unfortunately some ageism in the industry, you won't be spending 20 years in school.

I would still generally recommend holding a job of some sort during school if you can as that establishes that you are able to hold a job, follow instructions, and work with people. Even if that job is working for the school in a lab 2-3 days per week or as a research assistant for a professor, it shows you can hold a job.

Many students don't understand what education means to employers. To many students, a bachelor's degree means they know a lot, and a masters degree means they know even more. To an employer, a bachelors degree in CS means that they have the bare minimum skills that they understand what people mean. A bachelors degree in CS qualifies you for an entry level programming job, where you have zero experience and will need hand-holding for basic tasks. A masters degree means you know a tiny bit more and have done a slightly larger project.

Most masters projects are of a scale that an experienced professional could re-create the six month academic thesis within 2-4 weeks of professional work. To a student it seems like a massive project and a large, expansive, important epic creation; but a professional with 20 or 30 years of experience sees the identical project as an everyday task.