The way I look at it is that Meghan and Harry have chosen to be celebrities not royals. (Harry seems not have fully understood this choice, although the penny may be starting to drop).
As celebrities, they have the freedom to support whatever cause they wish, or drum up PR in any way they seem fit. I personally find the Uvalde association rather forced and distasteful, but if they can find families willing to associate with them, then OK. Go your hardest Harry and Meghan, and live your best (celebrity) life.
But what they cannot do to my mind is try and be Royals (capital R) at the same time. Prince Harry will always be royal (small r) as he was born into the family, but he no longer represents the institution. They cannot try to pass off these celebrity PR efforts as being somehow blessed by or associated with or adjacent to the Royals (capital R). They cannot and should not do this because the Royal family represents the Head of State and needs to be non-political.
Regardless of the ethical and constitutional ramifications, it seems to me that this is precisely what they are trying to do. Invictus/St Pauls/Birmingham demonstrates this - they want the veneer of a UK/Royal association to rub off on their personal PR efforts.
Given their persistence in this, the King Charles needs to respond in no uncertain terms. I believe a statement needs to be made whereby it is made extremely clear that Prince Harry and Meghan are acting on their own behalf, and not on behalf of HM or HM's Government.
I don't care what they do as long as they do not appear to be doing it in association with the Royals.