The rule is that your child cannot contribute to an HSA if he/she COULD be claimed as a dependent. It is immaterial whether or not your child is actually claimed as a dependent; the test is on whether or not he/she could be.
"My child had some income in 2019" Did your child provide more than half of his/her own support? Please review the rules for a dependent starting on page 25 in IRS Publication 17.
I suspect that you will find that your child could be taken as a dependent, so there is no possible HSA contribution, and you might as well claim him/her as a dependent and take the education benefits, too.
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