A distribution made in 2024 to correct a 2021 excess contribution must be a regular distribution, so coding it as a nontaxable distribution would seem to be an error made by Fidelity. This brings into question the type of distribution they think they made. If they actually did do a regular distribution as required under these circumstances and somehow coded it internally a nontaxable distribution, how they coded it internally is irrelevant and does not change the fact that it was a regular distribution that was eligible for rollover.
Perhaps you need to ask them to correct their incorrect coding. You need to make sure that they do not code the 2024 Form 1099-R with codes P and J or codes 8 and J which imply that they processed the distribution incorrectly. If they do issue a 2024 Form 1099-R with codes P and J or codes 8 and J, and refuse to correct it, you could file a substitute Form 1099-R (Form 4852) explaining that the distribution constituted a regular distribution, not a return of contribution before the due date of the 2021 tax return.
Because the distribution constitutes a regular distribution, the distribution is eligible for rollover no matter what Fidelity says. You should be able to deposit it into a Fidelity Roth IRA as a rollover no matter what Fidelity says about this particular distribution's eligibility for rollover by simply completing Fidelity's deposit slip (marking the deposit type as being a 60-day rollover) and sending it to them with a check. Fidelity doesn't really have any say in whether or not a particular deposit is a permissible rollover, particularly because the deposit slip does not ask you where the distribution came from. For all they know, the money could be coming from a Roth IRA that you have at a different custodian. It's your responsibility to determine whether or not a particular deposit qualifies as a rollover and Fidelity's responsibility to follow your instructions (unless it would be a clear violation such as making more than the permissible amount of regular Roth IRA contributions for a particular year). If somehow Fidelity won't accept the rollover, you could deposit it into a Roth IRA at a different custodian as a rollover.
