Given claims like "I have 70m doses that I can’t ship because they have been purchased but not approved. They have a shelf life of six months; these expire in April." from https://www.theguardian.com/global-development/2021/feb/14/w... it seems like claiming that the bottleneck is production needs some serious caveats....
I'm curious where these 70M doses are bought but not approved. As far as I can tell, AstraZeneca is approved all over Europe.
So it's entirely possible that the specific vaccines approved in Europe are supply-constrained, while other vaccines are in the situation described in the article. All that means is that saying that "the problem problem is production" is very specific-vaccine and specific-regulatory-unit dependent and needs to be evaluated carefully.