My Parent Recently Transitioned. How Can I Stay Connected With Her?

Apologies in advance if I'm getting any of the relevant terminology wrong. I'm trying my best! So just to keep it simple, I'm looking for any advice you all might have on how to stay connected and engaged with my trans parent. In brief, my father (bio male), late fifties, recently transitioned. She has a new name, a new look, and of course new she/her pronouns, told me it's okay to keep referring to her as my Dad/Father, etc. Cool, this doesn't bother me. I'm in my late twenties and have known lots of trans people before, so as a concept, this isn't exactly blowing my mind or anything. Here's where I'm feeling a little lost: I've always kind of operated on a "just tell me how you'd like to be referred to, I'll happily do it, and we can just proceed as usual from there" basis. That's served me just fine up to this point since gender (mine or anybody else's) isn't something that I've thought very hard about one way or another. To the point that I've actually not even mentioned my gender up to this point, come to think of it. I'm a straight guy, in a \*super\* conventional sense. I'm in a long-term heterosexual relationship, like to watch baseball, go fishing every weekend, that kind of thing. That's what comes most naturally to me. If you have a cousin or brother exactly like that, you've essentially already met me, as far as gender stuff goes. Maybe worth noting that I'm not any type of conservative, just in case that's part of that whole gender archetype. Anyway, back to Dad! When she transitioned, she picked up some new interests: New music tastes that speak to her current experience, makeup and clothing stuff, and a general desire to talk about that experience more. That doesn't bother me, but I have a hard time relating to any of it enough to actively connect with her over any of it. It's just out of my wheelhouse, and just getting the pronouns right doesn't feel like enough, since father-son seems like a more inherently gendered type of relationship than I've ever had with a trans friend. Something more feels needed in order to have a healthily-adjusted dynamic between a son and father who's a woman, but I'm not sure how to connect with the feminine stuff. Of course I can keep connecting with my dad over the same things we used to (she's pretty nerdy and I share some of those interests: board games, old sci fi movies, that kind of stuff) but I don't want to seem like I'm actively trying to avoid the bigger picture of who she is in the here and now in favor of the more-familiar past. That wouldn't be very mindful of her broader identity, I think, and I don't want her to be uncomfortable around me. All that to say, I'm feeling a little lost here, and if you, trans redditor, have ever been on the other end of a situation like this, I'd love to know what would make you the most comfortable. What could your clueless dude-guy family member do to help you feel at ease, accepted, and connected with in a genuine way? Apologies again if any of the statements, assumptions, or general presentation in here rubbed you the wrong way. Genuinely just looking for advice in an area I know very little about.