Sharing a few ideas that may help.
Health App\Activity\About Activity section mentions "brisk activity" as tracked for Exercise. As Alex mentioned above, maybe the pace and BPM didn't meet the Health App's algorithm minimum threshold for "brisk" to be considered Exercise Minutes?
https://support.apple.com/en-us/HT207941 mentions that Wrist Detection needs to be enabled for "Background heart rate readings (like resting and walking rates) won't be taken if Wrist Detection is off."
Or perhaps the Activity App did not sync the Exercise minutes to the Health App?
Another thought is that perhaps "Workout Power Saving Mode" is enabled in the Apple Watch app. If that's the case, then maybe the Exercise Minutes were not captured as thoroughly compared to when the "Workout Power Saving Mode" is set to disabled. Similarly there is a "Power Saving Mode" in the Apple Watch app Workout settings.
If you have AppleCare, may not hurt to call or chat with Support to see if they know about any problems, or settings required to record the minutes.