For anyone tracking this issue or who may come upon it later, my daily news site finally showed up in Google News about 15 months after launch. I paid a programmer to improve various back-end SEO stuff that may have helped, along with other improvements (including adding cookie and privacy policies); and I was also able to connect with Google News directly, which may or may not have helped. Anyway, it may have just been that I needed to wait 15 months and it would have happened anyway. From talking to other news publishers, many of them have found this to be the case in recent years (and Google News does not seem to care).
Jason Koebler of 404Media had a lot to say about this issue on Mastodon recently: Jason Koebler: "Google News is indexing and promoting websites th…" - Mastodon