Any investment gain or loss attributable to the $6,000 contribution is determined over the entire value of the IRA. Only if there was no net change in the value of the entire IRA between the time the $6,000 was deposited and the time the return of contribution is made with the return of contribution result in a distribution of exactly $6,000.
If the total balance in your wife's traditional IRAs is not much more than $6,000, it would make sense to keep the nondeductible traditional IRA contribution and do a Roth conversion of all of her traditional IRAs in 2023, leaving a year-end balance in traditional IRAs of zero.
