The King of England and his daughter-in-law saw each other privately before the latter announced her cancer on social networks. Charles III never hid his affection for Kate Middleton, his "beloved daughter- in-law" The sovereign was diagnosed with prostate cancer last February, the wife of his eldest son said she had a similar illness.
It also seems that it is not only King Charles and the Princess of Wales who have become closer during this difficult period. Both must manage their spouse's illness and honor royal commitments on their behalf. As such, it actually seems quite natural that they would hold hands.