I don’t think there are really callbacks or in-jokes in the recent Partridge stuff (obviously excluding the biography which obviously covers everything). MMM and This Time don’t seem to feature any.
It’s more that he’s (pretty organically, it seems) developed into someone with a complete media career and life in a universe only slightly removed from real life. I don’t know of any other characters who have done this to the same extent, and I think it works really well when they’ve added to it as they do every few years.
Obviously it’s not completely realistic (would he have been brought back from regional radio to co-present This Time? Probably not), but it’s close enough that every time we check in on him he’s moved on a bit in a way that basically makes sense.