IRAs are owned individually, so each spouse needs a separate form 8606. Form 8606 is required if you make new non-deductible contributions to an IRA, or if you withdraw money from an IRA and your IRAs contain non-deductible contributions. (This is true if you have any IRA account with nondeductible contributions; for tax purposes, you only have one IRA even if you hold accounts with different custodians.)
Your spouse will not have form 8606 for 2022 if they did not make nondeductible contributions this year or made a withdrawal this year. However, whenever your spouse does start to make withdrawals, they will need their most recent form 8606 from whenever they last made nondeductible contributions. Without that form, they may be unable to prove they have a partial basis, and all the IRA withdrawal will be taxable. Make sure that you and your spouse save all your form 8606s as long as you own any IRA. This is one exception to the general rule that you can discard tax papers after 3 or 7 years.
