I do agree partially to your line of thinking. When I as a young millenial was the age of today's young to middle gen Z (~late teens to early twenties) peak humor were ten hour long loops of Nyan Cat, Epic Sax Guy/Gandalf or Cantina Band with a side of Cheezburger Cat memes. Weird shit from a 30-something year old perspective.
My siblings and I are telling Dad Jokes to my niece at every opportunity and I can imagine those are your dominant form of humor when you have your own kids taking over your whole life.

However, there is another component to it, displayed by an oversimplified, slightly sarcastic analysis:

Boomer humor: I hate my wife.
Millenial humor: I hate my life.
GenZ humor: E

Of course, GenX is forgotten in this but from my experience, there is some credence to and a reason behind this.
Over time, relationships not lasting forever, divorces and marrying later in life has become more accepted socially, so elder folks might more often be stuck in unhappy relationship than younger people.
Meanwhile Boomers (and GenX) lived through Wirtschaftswunder, were less exposed to news and mostly had an overall more hopeful and positive expectations for life where Millennials grew up with the emergence of social media, more information available generally, being more exposed to crisis news and an increasing awareness about climate change and other threats to society.

This is not universal, there obviously was the Cold War and the looming nuclear destruction and this is mostly a western, often privileged white perspective, but still an influence on pop culture, memes, satire and humor.