It is possible that Prince Charles may have been disappointed that Prince Harry and Meghan Markle were not present at Trooping the Color, but there is no reason to believe that he would have sent a bitter letter.
Prince Charles has always been supportive of his son, and there is no indication that he has changed his attitude towards Harry since he and Meghan stepped back from royal duties.
It is also worth noting that Prince Charles is not the only one who was absent from Trooping the Color. Several other members of the royal family, including Prince Andrew and Prince Harry's sister, Princess Beatrice, were also not present. This suggests that the decision not to attend was not personal, but rather a matter of scheduling or other logistical reasons.
In conclusion, there is no evidence to support the claim that Prince Charles sent a "bitter" letter to Prince Harry after the King's huge success in Trooping the Color. This is likely a rumor that has been circulating online based on speculation and conjecture.