as a reference , I overhauled one of my bikes, a 2010 with integrated headset. Took it apart for the first time, so learning as I went, very simple, and after about 8 seasons of being ridden a fair amount, the grease was a bit dirty, but not bad, and I just cleaned and regreased, reassembled it all, keeping track of order of parts.

take photos if need be, to not mix up order, but pretty simple job.
I just used the thick phils bearinggrease I had around, then did the proper preload of the stem and all that.

if it wasnt used that much, and it feels all nice and smooth, its probably fine as is. My headset still felt smooth as always, but as I was doing the whole bike anyway, did the headset also. Bearing was a circular sealed thing, cleaned it up and greased all areas, some grease still oozes a bit out of it, just needs a wipe now and again.