They did. They blocked shipments from a factory in Italy. But this is a bad idea for all sorts of reasons:
1. No actual contract violation appears to be occurring. See my other comments.
2. Supply chains for vaccines are long and complex. The EU risks retaliation by other countries that block supplies to them in return.
3. EU has publicly proclaimed many times it hates the idea of "vaccine nationalism" as it calls it, by which it means countries blocking exports of things. Then they did it, it makes them hypocritical.
4. When governments intervene in third party contracts it makes that part of the world less safe to do business. The company is out of pocket and left to pick up the pieces with the customers. Companies hate that and it's ultimately companies, in a capitalist economy, who do the bulk of the work in society. So making it hard for them to do that means you're less likely to have such companies next time around.
Indeed EU already has a problem in the sense that most vaccines are produced by companies outside its borders, even if some factories are within it.
As for why they are suspending the vaccine whilst also demanding more of it, the suspensions appear to be political? AZ have claimed that the rate of blood clotting issues is actually lower in the vaccinated population than the average population, i.e. vaccines are not causing those issues, it's just coincidence. I don't really know how to interpret this claim - would that imply the vaccine is actually suppressing blood clotting problems? But so far AZ have a track record of making correct claims, and the EU does not, so I am inclined to believe them if that's what the stats say (they don't try to explain the lower incidence rates amongst vaccinated populations, just note that it exists).