This is interesting to read as I have 3 girls and all completely different.
I have an 11 year old who’s will occasionally play with her little sis but it’s definitely becoming a lot more grudged which breaks my heart as she is only 8 and would play all day every day if she had someone would.
However 11 and youngest DD are both very sporty and also both have ponies which takes up a lot of our time as they compete in various disciplines, have lessons and spend a lot of time outside and on the go with them and so the amount of free time after that is quite limited and it does give me reason to say to youngest it’s chill/tv/tablet time without feeling too guilty.
Eldest has just turned 13 and though obviously doesn’t “play” as such has definitely turned a corner in being a lot more sociable, interested in clubs etc and just seems a lot happier. She has now came back to her piano, will come and chat to us (often!!! 
) and is a very open book when it come to friends, worries, problems...it has however taken us a few years to get here.
I think 11/12/13 there’s a lot going on for girls, bodies are changing (or not) there is a lot of hormones brewing making them feel a 100 emotions at once, they are also trying to find a bit of independence as well as discovering who they are. I think it’s ok to take the expectation and pressure off a bit and let them come back to you in their own time. If it helps I always found instead of making an activity/time together so planned I’d make the most of smaller impromptu moments, my eldest loves me Dutch plaiting her hair on a Sunday night and always try to make sure it’s just the two of us and spend much longer brushing it than needed so I can have a no-pressure chit chat with her. (non eye contact conversations are great as this age) My middle daughter and I go and get the ponies in every morning and again this is our time to catch up, sometimes we will have a race and be silly, sometimes we don’t even speak but it’s lovely having that time with her.
Here are things my 3 are always keen to do together and things that have helped.
Sport/hobby find something she loves and get her out there doing it, go and watch, if she’s good push her gently at it. Make it “your” thing,
Baking. sometimes we bake together, but all 3 of mine now have a bit of independence in the kitchen and can make basic fairy cakes, scones, brownies etc. My rule has always been “as long as you tidy up after yourself” My eldest says has always found baking makes a rubbish day better and I have always felt that little bit of independence
All 3 of mine love dancing and singing and once a month we will have “a show” we will have a bit of piano, a gymnastics routine, some impro musical theatre, then entire greatest showman playlist and they absolutely love it, lots of silliness, a time to show off what they are good at and not tablets or phones in sight apart from the backing track
Shopping!!!
Games nights with snacks, fizzy drinks (mine aren’t allowed of normally) my girls at card sharks and we love UNO, 21 etc and have a lot of fun.
Finally I find it helps to keep up to date and embrace all the nonsense, trends, sayings, music etc that are forever changing.
I remember growing up I though my folks were on a different planet and would never get me as they didn’t have a clue about anything and didn’t even try, it made it harder to open up to them as I just didn’t think they’d understand.