Anne was in Scotland on official royal business and was able to get to her mother fairly quickly.
Charles was also in Scotland and hosting American journalist Jenna Bush and her crew, who were there to interview Camilla, as both share a love of literacy. Camilla’s plane was late so she had not arrived yet. Jenna described that chaos ensued after Charles took a phone call in his office saying his mother was suddenly ill, and he quickly left via helicopter. Camilla later met him at Balmoral.
I have read reports that the Queen had cancer, and she did look quite thin in the days before when she met with the new PM, but I don’t think that anyone was expecting her to die as quickly as she did
that day.
I did not know, and have never read, that Charles asked his sons to come. Makes sense, though, where he would be assuming the role of King immediately upon the Queen’s death, if she died. This does distinguish Harry from the other grandchildren, perhaps, as the son of a ruling Monarch.
I read a good article last fall (after the Queen’s death) about traditions at Balmoral Castle, and stag hunting’s been a massive one, for almost two hundred years (ETA and far longer in the Highlands in general). Some members of the RF didn’t like it (like Diana, and even PM Margaret Thatcher, if I recall) because there were often dead stags all over the place, and a lot hanging on walls, etc. With gillies involved (and after watching Outlander) I am not surprised at (what we see as) a dumb tradition like sticking a young lad’s head in the belly of a freshly killed stag.

But it is likely part of the Scottish traditions.
https://usakilts.com/blog/lore-of-the-scottish-stag.html
On the one hand, I’m surprised they’d do something like that to Harry, but on the other, I think even Charles would want to see his son(s) taking part in the traditions.