I wonder if girls are a bit more hormonal/standoffish/dramatic? I have teen boys and while they do spend a lot of time on their computers chatting to friends, they are still interested in doing things with us and they're not terribly dramatic, although the younger one can be. We don't tolerate rudeness but we do let the odd bit of sulking/irritation/eye rolling go. Choose your battles so that when you DO pick them up for being rude, they know they've overstepped the mark (even if they have to come back later to admit it and apologise it).
The stuff we do together: planning a nice meal to eat together, or watching a box set of something. We have a cut off of 8.30 for them to come and spend some family time with us eg TV (although don't enforce this if, for example, there is a prior arrangement with friends to do a Fortnite tournament or an online competition). We actually all 3 enjoy Bakeoff and Gogglebox, which is great as DH isn't interested so he goes off and watch stuff that only he likes. And vice versa. All 4 of us enjoyed Space Force, Line of Duty and stuff like Have I got News for you and 10 out of 10 cats does Countdown or whatever it's called.
I don't know if it helps but I work with teenage boys and have learned to not take things personally. It's not THEM talking or sulking, it's just their teenaged sulky self desperately trying to discover who they are/find their place in the world. It's a scary place at the moment, they need to be with people who understand what it's like to be a teen in 2021 during uncertain COVID times, and that's other teens!
I absolutely enforce "no phones in bedroom when it's bedtime" so they put them on charge downstairs, and 10pm is bedtime on a school night so they never really get overtired and grumpy. I think tiredness is a lot of the problem with teenagers, it makes them so irritable and short-tempered.
What I DO miss is as they've got older is their excitement about a day out somewhere. We used to be out all over the place during school holidays when they were younger, and even before COVID they stopped being enthusiastic about it (unless it involved food ha ha). Sometimes I think they come for a walk with us now just as a favour to US. 