I have to submit a copy of my 1040 tax form from 2020 for my daughter's school. The Turbotax form isn't signed and I wonder if it's legal without a signature?

When you e-file a tax return there is no physical signature on the line that says "Sign here." If someone wants a signed copy then you get a pen and sign it in ink for them.

The copy of your tax return is "legal" without a signature. The real question isn't whether it's legal. The question is whether the school will accept it. If they complain that it's not signed, do what xmasbaby0 said.