I don't think the EU have even approved it officially yet have they? And read another article just now saying what vaccines they have got, have been sent to vaccine centres without the correct length needles to extract the vaccines.
This is the problem with an organisation as big as the EU, and trying to agree everything as a political union, it all takes time. It might not matter for trade deals but things like vaccines in a pandemic you need to get a donk on, which is so difficult when you have soooo many different agendas and organisations to consult.
Also AZ are doing this on a not for profit basis. Add in potential legal fees and the cost of the vaccine is going to go up, impacting on the cost worldwide. The EU isn't going to come out of this looking like the good guys no matter what.
Also if they are going to cause issues like this, it's going to make companies, not just pharmaceutical companies, reluctant to operate in the EU. Isn't AZ a UK based company? I'd be packing that factory up and moving plant and people somewhere else out of the EU.