I think it is probably a bit of grandstanding on the part of the Sussexs', doubt it will come to anything beyond a letter written by a lawyer. Why announce to People that you have sent a 'letter from a lawyer' 😀, if it was truly a serious legal matter, they would be announcing a lawsuit not a 'letter from a lawyer'.
I doubt he will take it anywhere near a judge, a bit like his legal threat to the BBC when they reported he didn't ask the queen to use her nickname for their daughter. Lots of bluster for show.
Hopefully the mail will publish the 'letter from the lawyer' 😁