It doesn't work that way. Rolling over money from a traditional IRA to a 401(k) does not result in any tax deduction. Also, basis in nondeductible traditional IRA contributions is not permitted to be rolled over to a 401(k). A rollover from a traditional IRA to a 401(k) can only come from pre-tax funds in the traditional IRA.
Nothing on your wife's W-2 is permitted to be changed.
There is nothing that can be done with a nondeductible 2023 traditional IRA contribution that will reduce 2023 taxes or make the contribution deductible.
What you might be thinking of doing is obtaining a return of the traditional IRA contribution, resulting in the traditional IRA contribution being treated as never having been contributed. The distribution must include the attributable investment gain or loss with any gain being taxable on your 2023 tax return. Once distributed to your wife the funds are just cash. Your wife is not permitted to deposit these funds into her employer's 401(k), but, provided she is not already deferring the maximum permissible, your wife could increase deferrals from her pay in 2024 to increase savings in the 401(k) and reduce 2024 taxable income.