You're right that she gave a new meaning to being a "princess". She was only a princess because of who she married and at the time of her death, she was no longer royal and was classified as a "former" Princess of Wales. Diana, Princess of Wales denotes that she was once *a* Princess of Wales. It's the same with Sarah, Duchess of York. All of Diana's brother, Charles' ex wives could go by (first name), Countess Spencer until they remarried. It's the way ex wives that are no longer royal are styled. Diana was never a "princess" in her own right.
In her role as Princess of Wales, it was expected that Diana would work for the "greater good" in lines with what the monarchy was trying to accomplish for their people. She had to get express permission from her "Boss", the Queen for the things that she did and wanted to do. After the separation, four years before she and Charles actually divorced by order of the Queen, they were just keeping up appearances but after divorce, she became a former Princess of Wales that was once married to the heir to the throne. After her divorce from Charles, she dropped the majority of her charities and causes. "The 100 or so charities Diana supported during her marriage were reduced to six after her divorce. She continued to support these causes diligently throughout the remainder of her life, and perhaps most notably in the final 12 weeks of her life." She was working then on her own and for her own self and not as a "Princess of the UK". She was not part of the royal "Firm" and working for the greater good they strive to do.
https://www.upi.com/Archives/1996/07/16/Diana-quits-role-in-almost-100-charities/6983837489600/
Just thought I'd clarify this. It helps to know how the monarchy in the UK works and what is expected of their senior working royals that represent the Queen and the monarchy. She was a princess by marriage only and when that marriage ended, so did her being a "royal" end. She was stripped of her HRH and so was Sarah. They became "former" princesses at the time of divorce.
Hope this helps to understand what a "princess" is. ?