On a reasonable level, navel gazing (the figurative kind) is maybe better called self-reflection. I use DNA for genealogy, and it seems to me from the people I meet, that many get a healthier approach to our identity once we learn more about our genetic background. Identity politics, collective identity building around ancestry - identity building of all kinds really - needs simple stories. And the stories DNA tell are never simple.
At the bottom of the page there is a link to Sid Sijbrandij's cancer journey. He is one of the cofounders of GitLab. This is one of the coverages of his story: https://centuryofbio.com/p/sid
Well, yes, if done in excess. Hypochondria is a narcissistic trait.
Is going to your doctor or eating better food "navel gazing"? Predispositions to some diseases can be read from your DNA. Remember Angelina Jolie undergoing preventive mastectomy because she had a high genetic risk for breast cancer? Well, so do many non-celebrities.
Then there is the specific case of people who may suspect that their bio-parents are someone else, and there is nothing weird about wanting to know where you actually come from.