I raised Dd alone as an only child and I have to say I agree with pps!
Stop placating her and make it her responsibility - because it is!
I wonder does she have a mobile phone? A tablet a computer?
I would imagine she does and that you have internet? In which case absolutely NO excuse to be bored.
There are literally millions of games she can download, but you may want to encourage more educational quizzes and things like crosswords and scrabble. She can read via kindle app, I was a big reader as a child and would happily have my nose in a book for hours. At that age I was really too old for colouring BUT I found a way around that by drawing my own "designs" of clothes I'd like to wear (I rarely showed them to anyone as I'm not a great artist! But it kept me occupied).
My parents were great ones for puzzles and mum still gets puzzler every month, we were encouraged to do crosswords, word searches, word and number jigs etc I am a particular fan of logic puzzles which teach logical thinking, problem solving and excellent reading comprehension skills.
We'd also do things like knitting, cross stitch, making greetings cards etc including my brother who is a super speedy knitter now, making seasonal decorations (Christmas and Halloween are the obvious ones but we'd also do this for Easter and people's birthdays)
But also certainly at 11 she should have chores that are her responsibility anyway, her room should be tidy including dusted and hoovered, she is also plenty old enough to
Do her own laundry (and maybe even some of yours?)
Tidy, dust and Hoover other parts of the house
Cook meals
But also it's actually really good for their mental health to learn to relax! To not be over stimulated and always need that, they can maybe be helped with this with guided meditations and junior yoga.
Around this age my dd found she really enjoyed a good walk! She'd just zip off out with headphones on and walk around the park or along the seafront. She loved doing this and found it cleared her head, also helped calm her if she was stressed or angry. Good exercise too if they get a good "stomp" on.