I doubt that anyone outside her close family are really "mourning" her, but anyone who knew who she was and what she did will be sad.

She was a very "human", unfussy and unstuffy member of the Royal Family, who devoted the latter part of her life to teaching music incognito, and helping out with children's and homeless charities. She also took calls anonymously for the Samaritans, and worked at Lourdes following her conversion to Catholicism. Not performative Royal photo opportunities (she dropped her HRH title), but actual hard work on the coalface, on the quiet.

There's a story about when she promised a dying child one last visit, but was about to leave for an official visit to Australia. Against the advice of her husband, who was convinced she would miss their flight, she went to see him at Great Ormond Street at 0630 with a present of a koala bear, as she wasn't sure she would have time to do any shopping on her tour. She made it to the airport just in time, to be told the child had died shortly after she left.

She was President of the All-England Tennis Club and presented the trophies at Wimbledon for many years, including famously giving a tearful Jana Novotna a hug after she lost to Steffi Graff. She requested permission for the 12-year-old son of a murdered police officer to accompany her, only to be told by a stuffy official that only Royal children were allowed in the Royal Box. As a result, she boycotted the Royal Box for the rest of her tenure and sat elsewhere.

You'll have the usual ignorant comments about the Royal Family being irrelevant, parasites, rich bitches and the like. But she was a deeply caring person who shrugged off the royal shackles to do some real good in this world, never hiding her own emotion and vulnerability in the process.