As I previously explained, you already have a 6%, $360 penalty for 2022 for which you must file 2022 Form 5329.
Your excess $6,000 2022 contribution must be corrected by obtaining a regular distribution of $6,000, not a return of contribution. Tell the Roth IRA custodian nothing about this being a distribution to correct an excess contribution made in 2022. This distribution must be obtained before the end of 2023 to avoid another 6%, $360 penalty for 2023, so the sooner the better so that you don't miss that deadline. Because this distribution will be nontaxable, there is no conceivable reason to wait until the online version of 2023 TurboTax is available before you obtain this regular distribution.
By doing the recharacterization of your 2023 contribution, that contribution will be treated as if it has always been a traditional IRA contribution, no penalty. However, in 2023 TurboTax you'll enter the $6,500 Roth IRA contribution you originally made, then indicate that you "switched" this $6,500 to be a traditional IRA contribution. Doing so will cause TurboTax to prompt you to provide the required explanation statement.
