Bragging about it is a good PR and inspires confidence in your citizens -- even if you didn't actually capture anything. It's rather mystifying that they didn't try to present a strong face after this incident.
Back during the cold war, Daily Mail wrote a completely made up article about communist spies infiltrating sleepy English countryside villages, and people started calling up to report the spies they have seen on the streets. It became such a big deal that the government pressured MI5 to go and do something about it, so they "captured" and kicked out of the country a dozen or so communist spies found across the landscape of Britain, to a huge fanfare and celebration in the newspapers. Only years later it came out that that operation was entirely made up too, no one was actually ever found, captured and extradited anywhere, it was entirely just to satify the government and the public(who were riled up by a completely made up story in a trash newspaper).
Any information given would reveal what they can do, and by extension also what they can't, so to me it's perfectly understandable if they keep everything under wraps.
It escalates tensions for no readily identifiable reason. Like we’re not looking to pick a fight with China or Russia right now, and saying “hey y’all we captured a Chinese drone” sounds like a great way to push public opinion over a precipice and create a crisis that serves the interests of quite literally no one.
