"Our people first" is much more than nationalist chest thumping. When a plane is crashing from the sky, you put your own mask on before helping your neighbour, otherwise you risk both parties getting hurt (not just one).
This is the EUs bullying negotiation strategy which they employ everywhere spectacularly failing.
The EU accidentally leaked its own contract with AstraZeneca after trying to redact it. It showed that AZ were correct about the wording of the contract and the EU had been lying. There is no real disagreement about that anymore: the EU is on the wrong side of that dispute which is why there's been a lot of posturing but no court cases.
BTW several EU countries have stockpiles of the AZ vaccine they aren't using because their citizens aren't turning up for appointments or volunteering to be vaxxed.