1) Out of context, that TurboTax statement is misleading. That statement only applies to new traditional or Roth IRA contributions that are entered under Deductions & Credits, which these are not. The money was deposited into the traditional IRA as a rollover, not as a new contribution. Moving the $17.5k from the traditional IRA to a Roth IRA is a Roth conversion and is reflected on the code-2 Form 1099-R.
2) The $3.5k as well as the $17.5k that came out of the 403(b) are required to have been reported on a Form 1099-R, so you need to track that down with the 403(b) plan (not the Roth IRA custodian). If these were directly rolled over to the respective traditional and Roth IRAs, which seems to be the case because nothing was withheld for taxes, these would likely be combined on a single code-G 2022 Form 1099-R from the 403(b) showing a gross distribution of $21k. Unfortunately, TurboTax cannot directly accommodate reporting these rollovers to different types of IRAs by the entry of just one Forms 1099-R, so a single Form 1099-R reporting the combined distributions from the 403(b) will need to be split into two for entry, one showing the $17.5k and the other showing the $3.5k.
3) The code 2 on the Form 1099-R reporting the Roth conversion indicates that you were under age 59½, so none of the money distributed from your 403(b) would be an RMD, meaning that the entire $21k distributed form the 403(k) was eligible for Rollover. Three Forms 1099-R must be entered but the one reporting the $17.5k rollover from the 403(b) to the traditional IRA will be nontaxable.
