It's important to verbally bring it back to them after sharing your similar experience. Something like, "bla bla bla so yea losing my father was devastating so I can imagine the pain your going through right now." Then pause and let them talk again.

I think half the problem is that neurotypicals don't connect dots the way neurospicy folks do. It goes without saying to neurodivergent folk that the reason/purpose/meaning behind the personal story is to create a foundation for empathy and connection.