Yes, you will have to file Form 8606 because you made nondeductible contributions of $6,000 to your traditional IRA.
TurboTax is asking about the basis in your traditional IRA in 2019 and prior. Unless your rollover had also a basis (nondeductible, post-tax amount, nontaxable amount) you will not include the rollover amount in your basis. You stated there were no post-tax contributions in the IRA until you made the nondeductible contributions in 2020. Therefore, your basis will be $0 for 2019 and prior years.
When TurboTax asks about the value on December 31,2020 then enter the value left in the traditional IRA on December 31, 2020.
From The IRS:
Basis:
Your basis in traditional, SEP, and SIMPLE IRAs is the total of all your nondeductible contributions and nontaxable amounts included in rollovers made to these IRAs minus the total of all your nontaxable distributions, adjusted if necessary (see the instructions for line 2, later). (IRS Basis Form 8606)
Line 2:
Generally, if this is the first year you are required to file Form 8606, enter -0-. Otherwise, use the Total Basis Chart to find the amount to enter on line 2.
However, you may need to enter an amount that is more than -0- (even if this is the first year you are required to file Form 8606) or increase or decrease the amount from the chart if your basis changed because of any of the following.
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You had a return of excess traditional IRA contributions (see Return of Excess Traditional IRA Contributions, earlier).
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Incident to divorce, you transferred or received part or all of a traditional, SEP, or SIMPLE IRA (see the last bulleted item under Line 7, later).
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You rolled over any nontaxable portion of your qualified retirement plan to a traditional, SEP, or SIMPLE IRA that wasn’t previously reported on Form 8606, line 2. Include the nontaxable portion on line 2. (IRS Line 2 8606)
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