We know that as early as late spring/early summer, at the least, the Palace legal team was already at work, this being while the Queen was very much alive. In Nov. of 2021, the story came out that the Palace legal team was told that, yes, they can take legal action in cases of defamation/slander/libel.
The BBC World Service was discussing the past week and the analysts praised the Palace for it's swift action regarding the incident with Lady Susan. They went to add that Queen Elizabeth is gone and there is a new King and the Palace is no longer going to handle situations with kid gloves. It's going to strike back without any hesitation. They had praise for William and Catherine for their US visit and William's handling of this week's situation. There was mention of a US poll that placed William and Catherine at the top while the Sussexes were at the bottom of the poll among the US public, they didn't mention who conducted the poll.
I hope what was stated proves true.