He doesn't actually state what any of the supposed leaks are. IIRC, the only concrete evidence of a specific leak cited, was the one he accused Camilla of committing, following her first meeting with William - which was immediately and roundly disproved, the leak having originated with Camilla's PA, who spoke to her husband, who spoke to a journalist. The PA resigned at the time. Everything else is just vague, unspecified "briefings" against H (and later M) to gain "popularity".
The bridesmaid thing is about Kate being reported as the one crying, a report I believe (someone correct me if I'm wrong) Royal correspondent Camila Tominy says she got from 2 sources, neither within the RF. So the RF didn't leak a story saying Kate cried. However, Meghan says she was the one who cried and Harry says the RF should have corrected the Tominy story. Well, the RF didn't leak the first one, so why should they correct it?