I’ve done the DNA thing to identify my birth relatives (I was adopted). I found both sides. You’d be surprised at the number of people who “find” half siblings. I have 5, LOL. I used to think society was more conservative (even pious) in earlier generations and genealogy has taught me how wrong that impression was. Do you have a Facebook page? If you do, there are DNA groups on FB that are private (you have to be accepted to the group and no one except members can see your posts) and you can discuss your next steps in-depth with others who have been there/done that.
No, I don’t have FB, but 3 of my siblings do.