Come on OP, you're a childcare professional!
You can entertain a 6 yr old for 6 weeks and plan a party standing on your head. You are overthinking things.
Here's some of the stuff I used to do to survive over summer for free/nearly free 😊.
Swimming (our council has some free sessions)
Mini golf in local park is 50p
Picnics and daisy chain making.
Nature walk (take a bug net and catch insects to identify, go pond dipping).
Bike riding.
Book tennis court (our local municipal court is £2 per hour).
Do a project on the stars, visit local museum, stay up really late and stargaze, do pictures of the stars and planets and stuck on her bedroom ceiling.
Or dinosaurs etc.
Make a band, and play her fav songs with whatever instruments you can find in the charity shop. Make a stage from cardboard, film the show. Or do a musical show...like the greatest showman.
Baking
Sewing
Shopping...let her choose a meal, write the ingredients on her list and go and let her buy them.
Get to know every local park.
Visit local farm, some have ice cream Parlours, farm shops etc, and you can view the milking for free.
Gymnastics or Yoga, download a few videos and have a go.
Beach.
Catch a bus, mine loved this as they never usually went on buses so it was a big adventure.
Long tiring walks.
Lunch out, loads of places are doing free meals for kids over summer if an adult buys a meal.
None of it costs much.
I used to take them out in the morning and then in the heat of the afternoon they could chill in their paddling pool etc.
I honestly wouldn't spend a fortune on her birthday present. Memories are more important. You can pick up second hand bikes and skateboards really cheaply.
Maybe put some money in a savings account for her in lieu of her birthday gift, when you next get paid.