A person can own an HSA, and can withdraw from the HSA for qualified medical expenses, no matter what other coverage they have. Your FSA disqualifies your wife from making new contributions to an HSA, it does not affect spending.
All contributions count the same, whether from employer or employee.
Your wife was eligible to contribute in 2021, as long as she was covered by an eligible plan, and had no "other" medical coverage.
Your wife was not eligible to contribute in 2022, but no contributions were made, so there is nothing to correct.
Your wife was not eligible to contribute in 2023, but no contributions were made, so there is nothing to correct.
Your wife was not eligible to contribute in 2024, so the $3500 is not eligible. It is too late to use the "special procedure to remove excess contributions". You need to file an amended return and change her answers on the insurance question to "I did not have qualifying coverage all year". Turbotax will indicate there are $3500 of excess contributions, and ask if you want to remove them. Answer no (because it is too late). You will be assessed a 6% penalty on your 2024 return, and the $3500 is added back to her taxable income and subject to regular income tax (because it is not allowed as a tax deduction).
Your wife is not eligible to contribute in 2025. You should stop the contributions as soon as you can. Contact the HSA bank to remove the excess 2025 contributions only--this is a special procedure, not a regular withdrawal. (Don't even tell them about the 2024 excess. It is too late, and will only confuse them.) The excess 2025 contributions must be removed before April 15, 2026, along with any earnings (interest) attributable to the contributions. The contributions will still be on the W-2, Turbotax will ask if you removed them, you say yes. The $3167 is added back to taxable income (because a tax deduction is not allowed), but there is no additional penalty. The attributable earnings are also taxable income on your 2025 return as bank interest--even if you don't do the removal procedure until 2026, the attributable earnings are still taxable for 2025.
You now have two choices on how to deal with the $3500 of excess from 2024 that is still in the account.
1. If you plan to stop your FSA in 2026 and your wife will still be HSA-eligible in 2026, then leave the 2024 excess in the account. It will be assessed another 6% penalty. For 2026, your wife's contribution limit is $4400, or $5400 if she is over age 55. If she contributes less than the maximum, the 2024 excess will be applied to the 2026 limit -- basically you can "use up" the excess by counting it toward 2026.
Since the employer seems to give $1500 for free, your wife would contribute nothing extra voluntarily. Her total 2026 contributions would be $3500 + $1500 =$5,000. That's $600 over, so at the end of 2026 (before April 15, 2027) you perform the special procedure to remove $600 of excess. That will result in a $4400 contribution (combination of new money and old excess applied to the new year). There will be no more excess and no more penalties.
2. If you will not stop the FSA or your wife will not be eligible for the HSA, then you can remove the excess $3500 by making a regular withdrawal and not using it for medical expenses. This will result in the withdrawal being subject to income tax plus a 20% penalty, but it will remove the excess from the account so you don't get hit with 6% every year until you retire.
#2 is a very tax-heavy solution, so if you can use up the excess in 2026 by remaining eligible and contributing less, you will save a lot of money even though you will get a smaller tax deduction by not making new contributions.
