Diana was either 'The Princess of Wales' (or Princess Charles - which was never used), then after her divorce 'Diana, Princess of Wales', which was less stuffy than the more formal 'Dowager Princess of Wales'.
Meghan is 'The Duchess of Sussex'. Referring to her as 'Meghan, Duchess of Sussex' is a form of address following a divorce (as with Diana) or death of her husband. This is to differentiate her from any future wife of Harry (or wife of his son) who would hold the title 'The Duchess of Sussex'.
The term 'Dowager Princess of Wales' could not be used following her divorce. A dowager is - by definition - a widow. A divorce terminates any form of dower right.
The use of 'X, Duchess of Y' is problematic. It does not exist officially. In order to use the form of 'X, Duchess of Y', Letters Patent of HM The Queen are required (as in the case of both Diana, Princess of Wales, and Sarah, Duchess of York). The problem is the
Royal Family itself
. They use the terms quite freely. Statements issued by Buckingham Palace, Clarence House, St James's Palace and Kensington Palace refer to the both 'The Duchess of Y' and/or 'X, Duchess of Y'. It isn't a new phenomenon; both the Duchess of Kent and the Duchess of Gloucester have been referred to by the first name followed by their title since the 1970s. The Countess of Wessex is referred to as such today.