Most of the time, your FSA will disqualify your spouse from contributing to an HSA. Under the law, a medical FSA can be used to pay medical expenses for yourself, your spouse, and your dependents. Since it can be used to pay your spouse's expenses, it is considered "other medical coverage" that disqualifies your spouse from contributing to an HSA, even if you never actually use your FSA for your spouse's expenses.
Some employers offer a "limited purpose" FSA that only covers items not covered by traditional medical insurance, like eyeglasses and braces. A limited purpose FSA is not disqualifying coverage.
If your FSA is on a different plan year, your spouse might be able to contribute. For example, suppose your FSA plan year is July 1, 2022 through June 30, 2023. If your FSA is spent out on June 30, 2023, then your spouse is not disqualified for the remainder of 2023 (as long as you don't re-enroll). And your spouse could potentially use the "last month" rule to make a full year contribution for 2023.
