We tried this in
Greece. The reality is the IT systems underpinning most of this were very hurriedly put together as were the laws underpinning it.
To date most countries are only taking their citizens data , typically via social
security number to issue EU vaccine passes. It’s up to each country to decide how to address people in their country that fall outside the usual conditions , in
Greece that involved issuing temporary social
security numbers but we never then appeared in their vaccine database ( no reason advanced ) we checked with them every two days for 2 months.
Ultimately we went home and had the jabs and got the vaccine pass
You’ll most likely need to contact the country that administers the jabs or failing that convince your passport country to include your details on their vaccine pass database
Currently there’s no agreed way to add non EU residents to individual countries EU digital pass
There are lots of issues where people got one jab in one jurisdiction and one in another or where no national social security number exists etc.
These will no doubt get sorted in time , however the timescales are unknown.