I really loved the 2nd part of your post, @shenandoahvalley. The idea that the message sent was to indicate Catherine has King Charles stamp of approval seems valid.
That said, what's touching about a father-in-law saying such a thing about a daughter-in-law is the public declaration of the admiration he feels for whatever it is he said he's proud of. And, given he's the King, it's also a public warning: she has my stamp of approval.
From what I saw in the papers, he didn't say he's proud of her for dealing with the cancer diagnosis (it's not like she's got any choice, really). I read it as admiring of her choice to make a public statement, that public statement, the way she did.
There are very few people in the world who know what it's like to be under a microscope like any incumbent Princess of Wales. They will have been aware of the social media frenzy about her whereabouts.
I think he was expressing admiration for the way in which she handled that noise, whilst also dealing with a cancer diagnosis and treatment, whilst also trying to protect her public-facing DC from unwanted input, whilst also facing the not-unrealistic prospect that she and her husband might become King and Queen earlier than they anticipated. By any measure, that's a lot, isn't it?
There is news coming out with evidence that the bullying of Catherine was targeted. The entire family will have long known this. Thinking about how they can and should respond is interesting. The implications are really sad for their family and need to be treated carefully.
edited the quote to add breaks for easier reading with the bold text