I recommend General Finishes milk paint. It doesn’t look like the normal rustic milk paint but rather dries to a hard, almost enamel like finish.
Very minimal prep required.

How about using chalk paint? I've heard that's easy to use if you paint the whole surface, not just touch up.

I'd go after it with a Sharpie first.

For a table that isn't not prominently displayed and used:
If it's black paint, then lightly sand the top, wipe off, blue tape the edges. Find a black paint that matches then paint the entire top.
If it's a black stain (which is much easier) sand the top, then paint on the matching black stain. Once you can no longer see the white spots, get a spray clear coat. It comes in different finishes.

If the spots are small, paint markers would be easiest.

Title says it all.

I have a black side table/cabinet I purchased from BD decades ago, and the top has white spots on it (despite never having put a drink or anything on top of it).

Is there a magic paint I can use to just freshen it up without having to do a lot of prep?

If not, what’s the basic prep and what kind of paint should I use?

The piece is basically hidden in a far corner of the house, so it is rarely scrutinized closely. Nonetheless, I’d like to freshen it up so it looks better/brighter from a distance.