You are correct that the excess 2022 contribution is deemed to be in the Roth IRA. Because the October 15, 2023 deadline to remove the excess before the extended due date of the 2022 tax return has passed, the excess is subject to an excess-contribution penalty on Part IV of 2022 Form 5329. The amount on line 24 of your wife's 2022 Form 5329 carries forward to line 18 of your wife's 2023 Form 5329.
Given that your wife recharacterized the 2023 IRA contribution to be all traditional, I'll assume that your MAGI for the purpose exceeds the threshold where any Roth IRA contribution would be permitted, so the excess Roth IRA contribution for 2022 will remain an excess contribution for 2023. This means that the excess will also be subject to the excess-contribution penalty on Part IV of the 2023 Form 5329.
If MAGI for 2024 will be below the threshold and allow the excess to be treated as a Roth IRA contribution for 2024, that can be done to eliminate the excess. Otherwise, the exact amount of the excess must be distributed from the Roth IRA (with no adjustment for earnings) as a regular distribution (not a return of contribution. Because this will be a distribution of Roth IRA basis (or if the distribution is a qualified distribution), this distribution will not be subject to any tax or early-distribution penalty. If there will be any question as to whether or not the excess can be treated as a contribution for 2024, obtain the regular distribution and make a Roth IRA contribution later when it is known that the contribution is permissible.
