Worst-case scenario is that your dad does know and he's proactively asking you out to lunch to talk about it -- that's a good thing, even if it's uncomfortable in the short term.

I have tried to talk to my dad about it, and he just goes completely silent and doesn't engage and doesn't ask questions, so it gives the feeling that he's not listening, even if he is...

I would love it if my father (a public figure in a southern state) took proactive interest in my recovery. So far, not so much.

Let us know how it goes.

But he grew old, this knight so bold / And upon his heart a shadow / Fell as he found / No spot on the ground / That looked like El Dorado.