Yes, last time I had a run in with some government employees, they gave me business cards as well. They were a little less happy about me snapping pictures of them on my iPhone though.
Practically speaking, if you have a name you can contact the relevant department and ask for verification that the people are who they claim to be. IIRC it took 1-2 business days to get a reply by e-mail.
I think taking pictures of government employees is highly unethical. And it exposes them do DOXXING which is really not fair. Unless, that employee him/herself is behaving in an unethical, corrupt or legally incorrect manner....
Yes, you are correct to the greatest extent. Personal data and its privacy and protection applies to everyone. Even government employees.
That said, if you are aware how loose privacy settings are on most people’s phones, just having those pictures is a risk Quite like having pictures on the phone of personal documents. Especially in high-surveillance states, doxxing anyone is a legitimate risk.