Interesting figures about work of royals.https://www.cnbc.com/2019/01/03/meghan-markle-prince-harry-and-more-royals-who-worked-most-in-2018.html
Basically, in 2018 it's Princess Royal, Charlie, queen. Wills at 150 engagements was less then half the queens. Harry was less still.
Overall, the Royal Family as a whole carries out over 2,000 official engagements, entertains over 70,000 people at dinners, lunches, receptions and garden parties at royal residences, and receives and answers 10,000 letters
It's hard to get figures on hours worked and engagement count doesn't give indications of time at engagement or preparation time.
One point to note, as well as official duties they often spend time on their own business. For example Charles works a lot with the duchy of Cornwall of which he's the longest serving Duke. Duke of Edinburgh was heavily involved in running the royal parks and other matters.
I'm not saying they're necessarily working hard but I suspect they're not being lazy or purely privileged in their lifestyle but there's more going on in their life than simple official business.