I assume that you mean that the HDHP plan provided by your employer also covers your wife. Your wife is not your dependent.
Having an FSA in 2025 has no bearing your eligibility to contribute to an HSA for 2025 since you are already ineligible to contribute to an HSA for 2025 due to being covered by Medicare. However, if your wife is otherwise eligible to contribute to an HSA for 2025 due to being covered by the HDHP plan provided by your employer, your participation in the FSA in 2025 will make your wife ineligible to contribute to an HSA because the FSA can be used to cover your wife's medical expenses.
