"I understand your answer to say that any holding period time with the original custodian does carry over to the new brokerage firm." You misunderstand. See the first sentence of my previous reply where I underlined the word "not."
Since you have not said otherwise, I assume that the rollover in March 2022 established your first Roth IRA. That means that your Roth IRAs are not qualified until 2027. Because you met the qualification requirements in the Roth 457(b), the entire amount rolled over to the Roth IRA became contribution basis in your Roth IRAs. You can take that out at any time without tax or penalty. However, any earnings distributed from your Roth IRAs before 2027 (after having distributed all of your basis) will be taxable (but not subject to any early-distribution penalty). When entering any code-T distribution into any version of TurboTax prior to 2027 TurboTax you'll need to answer No to the question that TurboTax asks to determine if you met the 5-year qualification period for your Roth IRAs.
The IRS determines your 5-year Roth IRA qualification period as beginning on January 1 of the first year for which a Form 5498 indicating some type of Roth IRA contribution is filed with the IRS by your Roth IRA custodian, January 1, 2022, in your case.
