I'm American. So nothing will happen lol. We love Diana and Harry... William isn't our favorite brother but we have respect for him. We actually mourned Diana. We hate Charles and Camilla because of the Diana thing so one of their deaths will probably result to fireworks or something representing the disgust towards him, we're very vocal about who has our respect and who doesn't...because he doesn't have our respect if he died there would be some freedom of speech being practiced and dragging of the dead mans name.
HOWEVER: I think most of the US is indifferent to the queen. She's not adored but she's not hated. The Crown is kind of a popular show out here so there will most likely be some documentaries about her life, maybe some fox/abc 2020 coverage because people are curious but nothing will happen

The world will go on...
As annoying as it is, when she dies depending on our national news coverage, if we're having a light news day in terms or politics, she will most likely cloud our media platforms for a few weeks.
Americans find that royal stuff more fascinating so I imagine very few people being emotionally impacted but there will definitely be a peak of interest in Queen Elizabeth's life and what she was like. We don't want a monarchy but we're curious about it because the rejection of a monarch is the root of our shared history. We tend to be more fascinated about the system VS the actual monarchs as people.
She will not be missed on any personal level but we will find her story fascinating.
EDIT: also, there isn't a lot of information on her personality or what she's like as a person? I think some of her own people are still confused about what she's like as a person so if you can imagine how distant she comes off to foreigners.