@Maskless. Of course not having symptoms doesn't mean you've not got Covid, that's why you have to do a PCR test after a LFT of positive. And, of course, if you're correct and the LFT is a false positive, the child will be isolating for 10 days unnecessarily! So OP, just get the PCR test done.
Now, back to the lack of symptoms meaning a false positive. Our DS had no symptoms, we tested because we were due to go out with friends. He got a LFT positive. PCR test positive. DH and I had a PCR test as close contacts - negative.
Two days later I had a tingling in my arms and back. LFT test positive. PCR test positive. DH had a PCR test again as a contact. Negative.
Two days later DH did his normal LFT test. Positive. PCR test positive.
Apart from a sore throat plus the taste loss on day 4 or 5 and a pounding headache on day 3, none of us had any symptoms of Covid. Without the LFT we'd have been happily mixing with people until at least day 4 when the taste went.
Of course, as soon as the PCR test is done the test and trace people contact you and you have to give the name of contacts, where you've been and who has visited your house. So the cleaner will be contacted by test and trace as she'd have been in the house when the child was contagious - test and trace go back 7 days before you did the LFT.
Covid does not have symptoms for many people now. That's why LFT tests are important.
As for the cleaner now? I would let her know and keep her away. By law she shouldn't be coming into the home. If she gets it and can't work it's not just this household's money she loses.
As for the person who works as a TA. I work in a school. I got paid when we were in lockdown (all occasions) and when I had Covid. I don't see the problem in supporting another person, who doesn't get paid when they don't work, by a) keeping them safe if I know there's Covid in my home and b) paying them if I feel they need to stay away. It's called being a caring person.
And, as you'll have to isolate to OP, you'll have plenty of time to clean your own home...