Unemployment wants 8879 proof of signature

Form 8879 is not a "proof of signature." It's a form that is used to authorize a paid tax preparer to e-file your tax return for you. Form 8879 is not used when you file your tax return yourself with TurboTax. You don't have to authorize yourself to file your own tax return. If someone is asking you for Form 8879, either they think you paid someone to do your tax return, or they don't understand how tax returns are filed.

Form 8879 is not included in TurboTax because it is never used when you file with TurboTax. You could try explaining to the person who's asking for it that you filed by yourself. If that doesn't work, try asking to speak to a supervisor or other higher-level person who knows more about tax return filing. The unemployment office must see a lot of people who don't use a paid tax preparer, so they should be familiar with the situation. You just have to get to the right person.

That does not exist for self-prepared tax returns.    A 8879 (signature authorization) allows a paid professional to e-file a tax return on your behalf.    You are filing your own tax return and are your own preparer so you cannot authorize yourself.

https://www.irs.gov/pub/irs-pdf/f8879.pdf