Student loans, in his own name (you did not co-sign) are considered support provided by him. So, you are correct; student loans do count toward support, and you cannot say that you provided more than half his support. You cannot claim him as a dependent.
Did your son turn 24 in 2020? The earned income support rule applies to students under 24. It has to do with non working students under 24 claiming a refundable tuition credit. Earned income is not relevant to the dependent issue.
There are two types of dependents, "Qualifying Children"(QC) and standard ("Qualifying Relative" in IRS parlance even though they don't have to actually be related). There is no income limit for a QC but there is an age limit, student status, a relationship test and residence test. Only a QC qualifies a taxpayer for the Earned Income Credit.
If your son was over 23 on 12-31-19, he cannot be a QC. The support test for a standard dependent is that you (the parent) provided more than half his support for the whole year.. The support test for a QC is whether he provided more than half his own support. That distinction may not make any difference in your case. But, scholarships (as opposed to loans) are third party support and not support provided by the student. Parents can frequently claim a 23 year old but not a 24 y.o.
Full rules:
https://turbotax.intuit.com/tax-tools/tax-tips/Family/Rules-for-Claiming-a-Dependent-on-Your-Tax-Ret...
