It won’t. The Cambridges are still popular so it will be fine. All they have to do is do another strong PR campaign and Harry will be back in the good graces in no time. Seems like he gets immunity just by being Diana’s son tbh.
Regarding any BRF vs Megs PR fight: it’s not an even match. It’s basically a nuclear bomb vs sticks and stones. Megs can’t win that fight because she’s not popular enough in any country–UK or USA–to have enough resources to win.
Megs isn’t on par with Diana. She hasn’t achieved the reputation, standing, or respect that Diana did going into the War of the Waleses. Megs vs BRF is going to come up with a huge loss for Megs. The only reason she’s able to engage on any level with the tit-for-tat reporting that has been going on recently is because BRF members–Queen, Charles, William, etc.–are being nice because she’s married to Harry.
Megs will bear much of the fallout for this relationship/marriage demise because she doesn’t have as much of a long-established reputation in the media.