@BuggerBognor (great name), just thinking it through in more detail...
The EU's shortfall is 60 million doses in Q1, and approx 110m in Q2. 170m doses in total.
We know pretty much the entire production of Az from within the EU is going to the EU, topped up with supplies from the US.
If the Belgian court orders Az to increase supply from within the EU then that means Az opening new manufacturing sites and production lines. Not a quick process, and something that presumably would happen faster if the EU supported it rather than litigating for it. In any event, it would be useless in securing additional doses in the near future.
We know the UK's total production is about 2 million doses/week. Let us assume that the Belgian court orders Az to divert all of that into supplying the EU contract (unlikely, because as you say I don't see how the contract binds AZ UK) AND let us further assume the UK doesn't block those exports (also unlikely) or tie them up with further legal wrangling. At 2 million doses a week it would take 85 weeks to make up the Q1 and Q2 deficit alone. By which time the EU will be rolling in Pfizer. As a method of securing vaccines, it's totally meaningless.
The Serum Institute in India are manufacturing enough to be meaningful. However, the Indian government have already effectively blocked exports (because they're burning bodies in car parks) and I suspect would take little notice of a Belgian court. And I can't see that Belgian court would be so daft as to try and order an Indian company to forcibly export their product.
The other big manufacturing location is the US. If anyone thinks the US will take notice of decisions in a Belgian court then I have a bridge to sell you.
So the stated goal of this litigation - to secure the vaccines that Az promised - is clearly farcical. As you say, we need to know what relief is actually being sought, because what's presented just doesn't add up.