From what I can see, Turbotax only allows you to choose sources of benefits as "Government (From 1099-G), Non-Government," and "Both." PUA is from the government, but I can't get a 1099-G, so how do I report the PUA income?
I suspect you are looking at the wrong place on your state's website if you think the state will not give you a 1099G for unemployment. They more likely are saying they will not issue one for a state or local refund unless you itemized.
UNEMPLOYMENT COMPENSATION
Unemployment compensation is taxable on your federal return.
You will have to enter a 1099G that is issued by your state.
Some states will mail out the 1099G. Or you might need to go to your state’s unemployment website and use the password, etc. that you have been using to certify for weekly benefits to get your 1099G from the state’s site.
Enter your 1099G in Federal>Wages & Income>Unemployment
Go through the screens very carefully, making sure to enter any federal/state tax you had withheld from the unemployment.
STATES THAT TAX UNEMPLOYMENT BENEFITS
AZ, AR, CO, CT,, DC, GA, HI, ID, IL, IN, IA, KS, KY, LA, MA, ME, MD, MI, MN, MS, MO, NB, NM, NY,NC, ND, OH, OK, OR, RI, SC, UT, VT, WV, WI
STATES THAT DO NOT TAX UNEMPLOYMENT BENEFITS on the state return
AK, CA, DE, FL, MT, NH, NJ, NV ,PA, SD, TN, TX, VA, WA, WY