With my son (now 14) we haven't had any hard rules about screens but went with the "keep them busy" approach suggested already by one or two posters.
I used to think my son was too busy with activities and his life too structured but then his favourite thing ever became "hanging around down the park" and while that is fine now and then on a nice day he wanted to go daily and in all weathers. I was worried that too much hanging around would lead to mischief/trouble and terrified he would get hurt/attacked. So I have decided to keep up lots of structure while we can.
I'm curious why you said OP that you have a child that is not suitable for scouts? It's active games, chippy walks, cooking on fires, home made water slides on hills etc. What's not to like? And for £12 a month! Thank you Scout leaders!
Local chess club (free) learned to play by using chess kid on the ipad.
My son is into playing music (although lessons £££) he self taught the first two years using simply piano on an ipad and a cheap keyboard - but knock on effect of playing opens up free/cheap open mic nights, band practices, orchestra, practice at home.
Duo lingo - lots of kids I know like to do a few minutes of this each day snd "keep their streak".
Park run - not been over winter (free)
Other ideas we do now and then: swimming, bikes (not me but with his dad), family walk somewhere.
If they have one activity in an evening by the time they have tea, homework etc not too much time for screens before putting them away for bedtime.
I think even when kids are on screens you can sometimes tell them also to get off tic-tok type content and for example use duo lingo, watch you tube etc of something they are interested in that is educational like different countries, learn a skill e.g. chess kid, simply piano, guitar learning app, digital art, programming, making websites. Playing games with mates online is social and they can have to work through conflicts in games like minecraft.
All that said coming out of a long rainy winter has been a challenge to stay busy in the holidays as nothing much to do outside.
You said your child plays a sport OP. Do they love their sport? Can you get them playing at organised venues regularly to keep them busy and socialise?