3 bn PER year. Trust me. You may have to get vaccinated every year. Don't get me wrong, the strategy makes sense. Still not very encouraging.
The real reason the EU needs this kind of capacity is that the current EU vaccination campaign is going very poorly. Most of the population will only get vaccinated late in summer and autumn, so the yearly capacity needs to be appropriate to at least get it done this year and before the next flu season.
Oh, and the EU produces vaccines for a lot of others like UK, Israel and the US, as well as most third-world-countries. Imports into the EU are neglegible.
Hint 2: ""Quite often vaccines are more effective than natural immunity but we might need to vaccinate everybody every year, or two or three, for quite some time and maybe forever."
https://news.sky.com/story/covid-19-will-we-need-an-annual-v...
Sorry to break the news to you but it is unlikely the world will be what it was.
https://www.reuters.com/article/us-health-coronavirus-eu-vac...
"The European Union aims to increase the region’s COVID-19 vaccine production capacity to 2-3 billion doses per year by the end of 2021"
Hint: The EU has about 400 Million people