The second layer of Unemployment comes from Pandemic Unemployment Assistance. Some states have this available, but not all. It is being rolled out slowly and on different timetables (see previous post to check status of different states).
WHEN PUA is available in your state, that is when your work as a 1099 Contractor comes into play and will need to be reported.
Once you are in the system, and your state has begun Pandemic Unemployment Assistance, THEN you should begin receiving the extra $600 per week for up to 4 months in addition to your qualified unemployment amounts.
File in the state where you live even if your 1099 gigs are scheduled for other states.
Once the state has their Pandemic Unemployment system ready, you can apply for unemployment as a 1099 CONTRACTOR without having W2's in your work history!
Check if your State's Unemployment System is ready for Pandemic Unemployment at this time: HERE