Ctmav is the Korean made Astra zeneca. That’s what I got in my first shot in Taiwan. Yellow booklet has a batch sticker az 1 batch ctmav 509-cdc
When I got my second shot in Cyprus, this time abx4044 - which is ab - hence EU produced, they asked me what the first shot was, I told them AZ = Astra zeneca and my EU green pass shows valid, it doesn’t list the first vaccination however, but says that the second vaccination was the second.
If you aren’t vaccinated inside the EU, it will be hard to get green pass no matter what you were vaccinated with anyhow. Many countries issue green pass from the national health insurance website, so tourists cannot get it. In Cyprus e.g. you have to download it from the health insurance website membership area. No way for a tourist to get the EU digital covid certificate here. Likely you can get a printed out version at the place of vaccination, If you were vaccinated Here without health insurance. Not sure how well that works out. Likely very problematic too.
In Germany they didn’t register the first vaccination, so you go to pharmacy show them your vaccination passport, and they issue it. As they get 15 euros for this from the state, likely only available to residents.
At the borders I am sure the officers won’t bother to check what batch you have. Show them anything that looks like a vaccination passport, at best they check it hast two stamps/dates/stickers plus 22 days and you’re fine.
The EU certificate is anyhow only an alternative to the vaccination passport.