You apparently have a factory primed door. It could be an alkyd or acrylic
prime coat, but the kind doesn't matter vs what paint you chose as a finish
coat. We used exterior acrylic water based paint over our metal clad door,
which was also pre-primed. Fine sandpaper lightly first, dust off, clean and
rinse thoroughly, dry, then paint. We used semi gloss on it, as it may be
easier to keep clean vs flat or satin. We left the door slightly ajar for
several days so the rim and edge of the door would dry, and not stick once
it is closed against the weatherstripping and jamb.

What type of paint do I use? I would like to paint it in-place.
Latex? I have no docs left that came w/ the door - the instsallers
left nothing - can I assume it has latex primer on it?