Form 8606 will not be generated to report non-deductible contributions to an IRA unless you indicate in the program that you did that.
If you were able to make a non-deductible contribution to an IRA, you should have seen a screen in TurboTax that said Choose Not to Deduct IRA Contributions:
So, it is possible that you aren't allowed to make an IRA contribution in 2024. This could be because you don't have sufficient earned income to do so or you have already contributed the maximum allowed for the year ($7,000 plus an additional $1,000 if age 50 or over.) You can learn more about IRA contribution limits in this IRS article.