Goodness - I teach my children about body autonomy, but if my 4 yo had true body autonomy, she'd eat chocolate for every meal, followed by ice cream for pudding and the occasional cracker or soreen for a snack.
Sometimes, you have to do something which is for more than emergency / lifesaving treatment, some times you make a best interest decision balancing up what's needed to keep your child and your family safe and well. I pinned her down for her pre-school vaccinations too, she didn't get a choice in those.
Of course I'd keep my sick child at home, but not for 10 days and since the current guidance is if you have a symptom of covid you should isolate for 10 days, I reckon a bit of cajoling to get a pcr test is probably better for her than not being allowed to leave the house for 10 days. And it's probably better for her to have a roof over her head and food on the table than one of us end up losing their job to be at home with a not unwell child for 10 days every time they get a temperature during autumn and winter.
It's also about teaching that with rights, come responsibilities and consequences of decisions - yes you have the right to absolute body autonomy if you don't want to test, but with that comes the consequence of being legally required to isolate if you have symptoms. With sunscreen - ok you don't want it on, but it means you have to sit in the shade all day while your friends have fun.
It's not cajoling, it's making best interest decisions for small children who don't have the ability to give informed consent or understand the potential consequence of not being tested.