As with any nonqualified distribution from a Roth IRA, TurboTax prepares Form 8606 Part III to calculate the taxable amount. When you click the Continue button on the Form 1099-R Entries page, TurboTax will ask for your basis in Roth IRA contributions and conversions to complete the entries on Part III needed to calculate the taxable amount (which will be zero in your case); yes, you must provide this information. TurboTax will also use the information to determine that there is no penalty to be reported on Form 5329.
The Roth IRA custodian(s) have sent Forms 5498 (as well as Forms 1099-R reporting distributions that would have previously reduced your basis to some extent) to you and to the IRS to document the contributions and conversions, so the IRS already has the information needed to substantiate the entries on Form 8606 Part III. If you don't still have these documents yourself, it might be difficult to get copies from either the IRS or from the IRS custodian going back 20 years. Approximating the values might be your only option.
Be aware that distributions from your Roth IRA that are not rolled over eliminate the possibility of future tax-free growths on that amount, so a Roth IRA distribution should generally be a funds source of last resort.
