I don't imagine Charles ever had the least objection to Uganda attending, but I'm not sure where a "misunderstanding" comes into it when their spokesman placed no blame on him for their withdrawal - indeed, the reverse
That's not true.
This is a quote from the BBC article in the main Uganda thread.
Uganda is pulling out of the Invictus Games, a sports event for wounded military veterans run by the Duke of Sussex, only two months after the country said it would join.
General Muhoozi Kainerugaba, chief of defence and son of the president, made the announcement in a social media post on X.
He said the decision to withdraw from the games was "in order not to be construed as being opposed to His Majesty King Charles III".
Also.
A report in The Times newspaper quoted the general's concerns about the "Harry-Meghan nonsense", suggesting this was the background to the decision.
"In order not to be construed as being opposed to His Majesty King Charles III of the United Kingdom, whom we deeply revere, Uganda hereby withdraws from the Invictus Games," said the general in an overnight post.
"We shall not participate in anything that does not have His Majesty's approval."
So the statements very clearly referenced King Charles. As such, Charles' response is quite appropriate. I don't see it as 'indulging' Harry at all, rather just making it clear that he has no objection to Uganda being involved in the IG. As other posters have remarked, he'll likely have had guidance from the Foreign Office about this too. Had he not responded, it might have been assumed that he did indeed object to Uganda's involvement.
Little to do with Harry. More to to with international diplomacy, something neither he nor his wife have a clue about.