My DD is 11 and like yours, loves screentime. I can sometimes engage her in crafts if it's things she's seen on youtube (eyeroll) A walk is another way to engage her, especially if we stop for coffee.

I was wondering the same thing today, re my youngest DS who spends more time looking at a screen than I'm comfortable with!

I came across a website called Treasure Trails that has hundreds of trail maps that you can print at home, to explore places all over the UK, with themes like spy trail or murder mystery. Going to try our first one this weekend - would that sort of thing interest your DD?

What does she belong to / go to outside of school ?
When ours were 10, we didn't really 'entertain' them as such - they did things with cubs, for example.

I got my DD into geocaches It was useful to head out when the winges hit .I added stopping if we saw something that would make a good photo.
She now has a good camera that she saved up for and we still head out in the car going down roads we have never been down before or saying next right/left.or stopping and going for a walk .
I've found that she using her screen to fill in when I'm busy so I have to make down time for her a bit more.
However she's a teen and it will always be wrong except when your idea becomes theirs.

When my ds was that age we used to go to lots of English Heritage places, eg. Dover Castle. Lots of extra events/workshops over school holidays.

Got the annual ticket through Tesco points.

My 10 year old is busy with rugby/cubs/guitar +/- band/trampoline in the garden/ meeting friends and birthday parties etc.

He does enjoy a bit of screen time but that’s in between everything else!

Once mine were that age, I found them less eager to do whole days out but happy to do something with me for 2-3 hours such as crazy golf, bike ride, treasure trail (mentioned above), bowling, driving range or even a walk or museum trip if involves pub lunch or cake at cafe.

Mine (now 12 and 14) know my rule is each day has to involve some fresh air (unless pouring with rain) and some exercise so they can choose what to do but can’t choose doing nothing!

Apart from screens, what else is she interested in?

Getting outside for walks with an added element, as pp have already suggested. See National Trust's 50 Things project for more ideas.

Re-visit some of the places you went to when she was younger and not old enough to appreciate in the same way.

Crafts - sewing with a machine, knitting, pottery painting, card-making.

Use tech in more creative ways, e.g. stop-motion animation, reading the same (Kindle?) book separately and then discussing. Baking (find a recipe online). Photography. Music. Learn a language together.

With those of her friends who aren't available due to working parents, are you willing to have them over for the whole day? My DD is just about to turn 10 and we have one of her friends over from 7am - 3.30pm tomorrow and had another on the inset day last week from 8am until 6pm. In both cases, the parents initially declined as they thought I meant a more regular play date of a couple or a few hours (which is what I did initially mean) but, when I realised the situation & after chatting to my DC, extended it to cover the full time that they were at work.
Last week, they played at home for a couple of hours, we went swimming, they helped make lunch, we down to the park where we met other friends and then came back home for a couple of hours. Tomorrow, apparently, they are making slime and doing junk modelling and, if there is time, want to play board games, some of which may involve me. If it all goes wrong (we haven't had this friend over for more than a couple of hours before), we'll head out for a walk or something. If they keep each other occupied, I will clear out the garage and finish my book.

I have a 14 year old son!! Nightmare lol

We have “family nights” or days out where I have no phone rule hahaha. Adults included!! So once a month we’ll go out to eat and one of us chooses where.... and we take it in turns every month. So that’s nice to sit down and talk properly without him going off to his room as soon as he’s eaten .

We also go to the cinema a lot. As we all like films. We all watched the new John wick film last weekend.

We have random days out too.... the beach is always a good bet!! Especially ones with good arcades lol

Trampoline parks??

If your DD like sports I would find an activity or two to do over the holidays or- tennis /
Swimming which you can sometimes do for a morning only up to 5 days a week.
If they are doing some exercise for half the day I am less concerned about the screen time.
Museums often have free activities in the holidays which might still be age appropriate.

Today and tomorrow my 11 yr DS is kayaking from 9-4 pm. Great as he is out side in the sunshine and with a lovely friend.

There is so much to choose from but it's expensive so I seem to save up a lot for the holidays. My children tend to do -
Sailing courses, riding, trips to the beach, tennis, cinema, bowling, pottery painting, visiting friends/ family, shopping, lazy days at home, reading and relaxing, dog walking (a lot!!!) helping to clean and tidy the house...