The version of TurboTax will not affect whether your return is accepted or rejected. However, in your case, I honestly hope that your return is rejected, because it will allow you an easy way to fix what I perceive could be a significant reporting issue that affects your tax return. Here's why:
You state that you only received a W-2 and unemployment, which is reported on Form 1099-G. If that's true, your return should have qualified to file using TurboTax Free, and not TurboTax Self-Employed. In fact, the only thing that would require TurboTax Self-Employed would be self-employment income, which is often reported on a different type of Form 1099, a Form 1099-NEC (sometimes Form 1099-MISC).
How does this affect your return? Self-employment income is subject to self-employment taxes, which is the equivalent of an employee paying Social Security and Medicare taxes, and is approximately 15% of the amount of self-employment income. However, unemployment income is not subject to this tax. So if you have accidentally reported this income incorrectly, you are paying more for the program and you are paying more in tax also.
If you have already submitted the return, we won't know whether it is accepted or rejected until February 12 when the IRS opens e-filing. If the return is rejected, you can correct the mistaken entries by deleting the Schedule C and re-entering the 1099-G as unemployment. And if it rejected, you can attempt to contact customer service to see if your account can be re-set to correct the mistake and maybe receive a refund to lower the level of program. (No promises there, by the way. We have no say on refunds in this public forum).
If it is accepted, your recourse will be an Amended return. Please see this link for additional information: How do I amend my 2020 TurboTax Online return?
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