In England at least, it was impossible to get tested unless you met an incredibly specific set of cirumstances and locations. After that, you could only be tested if you were admitted to hospital with severe breathing difficulties.
By the time testing became available, any of the significant number of staff who were off sick by the end of March or sick over April were beyond the point at which testing was reliable. and to be counted as pupil-staff transmission, the child would also have had to qualify for testing under those incredibly narrow requirements.
We had kids after half term coughing their guts up after a sibling or parent had come back from about 3 miles outside the geographical range for testing. After they'd been sent home, there was no confirmation of infection, as the person who had gave it them hadn't been tested. And then more kids got ill. And staff. Still no testing as they hadn't been to Italy. And then more got ill. Still no testing as they weren't in Intensive Care. And then everything closed down in the NHS and you couldn't get seen at all unless you were turning blue.
The structure made it impossible to say that anybody had caught it at school. Which is why, even before people say, 'Ah, but you must have bought food or passed somebody in the street/used a petrol pump, it doesn't have to be the coughing, feeling sick, blistery fingered, high temperature kids you were in the same building as for 8 hours a day that gave 'something' to you', it's impossible to say they did - and it's equally impossible to say with any accuracy that they didn't.