Each and every conversation with hints is made into a game of charades just to avoid saying Burke is Sages daddy, it's a constant avoidance of that fact even when it would make perfect sense to mention that fact first in these conversations.
Sage being Burke's daughter? Nope, not much sense there, just the realisation people around you know it but they've been playing this game called "don't say it's her daddy"... Not gonna call it bad writing, just not gonna agree it's a good twist.
There's no "How did i not see this?"... only "how the heck you gonna make me believe nobody told this?"
I agree it's a little sloppy execution of the twist, but it's not immersion-breaking. Nobody told because everyone assumed the Mc knew, it was common knowledge. I can relate to that. Let me explain:
I come from a family of teachers. My dad was a teacher in my junior high school and my maternal uncle in my high school. From day one almost everybody knew who I was related to. I never bothered telling any new friends I made, because I assumed they knew already. It was a given, I never thought about it. So Sage or anyone else not telling Fuckface is something plausible, to me at least.
Now, the Mc not knowing the last name of a girl he is fuckbuddies with or romantically interested in? That's harder to swallow. Maybe he knew but thought there was no relation? I'm not a native English speaker but I believe Burke is a quite common surname in the English-speaking world, or at least not rare. And we are shown that Fuckface is a little boneheaded sometimes.
Like I said... sloppy, but not outright implausible