Meaning of "What are your new coordinates"?

The relevant literal sense of "coordinates" is geographic coordinates, specifically latitude and longitude, nowadays sometimes called "GPS coordinates".

But it's really just a humorous way to ask where you are now; (s)he's not really expecting coordinates back. You can either reply with a normal-person description of your location (such as "I'm in Paris", or "I'm in a suburb of Washington, D.C.", or "I'm in London, near the Eye", or "I'm in a secret bunker in an undisclosed location"), or double down on your colleague's joke by looking up your coordinates and sending those instead!

Or it is an idiom and he/she means how things are going at the new country/workplace?

That's not what (s)he means, but it would be very reasonable to say a bit about that (such as "It's been an adjustment — did you know that some Americans walk barefoot in the street? — but overall I'm really loving it!").