It's included in taxable income in box 1 of the W-2, but then a deduction on Schedule 1 line 13 would take it out of taxable income. The result is largely equivalent to you not having the funds taken out of your paycheck by your employer but your spouse instead just making the same HSA contribution directly to your spouse's HSA, except that when made through the employer the employer must still include the contribution amount with code W in box 12 of the employee's W-2.
I suspect that the reason that the IRS wants these contributions not to be excluded from box 1 of the employee's W-2 is that the amount in box 1 (the employee's "compensation") might be used on someone's tax return for purposes other than determining total income on (2022) Form 1040 line 9. For example, the lower amount that would otherwise be in box 1 of the W-2 could limit how much the employee or the employee's spouse could contribute to an IRA. If the employee earns $5,000 (and neither spouse has any other compensation) and has the entire $5,000 diverted to the spouse's HSA, the fact that the $5,000 must still be in box 1 of the W-2 which allows IRA contributions of up to $5,000 while still getting the amount of the HSA contribution excluded from income by the HSA deduction on Schedule 1. If the HSA contribution was instead excluded from box 1, leaving $0 in box 1, no IRA contribution would be allowed by either spouse.
