1099 solo practitioner: do I qualify based on my net income or gross income?

Qualification would be on your net income.   The child tax credit  (CTC) is  limited to your tax liability. The CTC is a non-refundable credit and can only reduce your income tax to zero.  It can not help you beyond eliminating your tax liability.  However; if you have more than $2500 of earned income (Net Self Employment Income), some or all of it is usually given back to you thru the "Additional Child tax credit".

2023 & 2024 Child Tax Credit 

Qualify for what?  If you file your 1099 sole proprietor on Schedule C it uses the Net Profit to determine things like IRA contributions.  You pay tax on the Net Profit.  The Net Profit is part of your AGI to qualify.