It depends what kind of high deductible health plan you have. You said you thought you had up to $7,300 which indicates you were on a family plan, not a self-only plan. But all your math is based on self-only plans.
If you have a family plan, either spouse can contribute to their HSA and the contributions are collected. The only rule is that the additional $1,000 contribution must be placed in each spouse's account if you are contributing the max and both spouses are 55 or older. It doesn't matter if each spouse gets $4,650 or one spouse gets $1,000 and the other gets $8,300 if you are covered by a family plan all year. Either way is fine and won't lead to an over-contribution. You just can't have one spouse deposit all $9,300.
In your case, at least 8 months will be a family plan, which means your eligible contribution would be $7,300 *8/12 + $1000 *8/12 = $5,533. In that case, you're still okay. If you want to make additional contributions for your wife's HSA, she would need to still be covered by some sort of high deductible health plan after you go on Medicare.
If you have an individual plan, it does look like you have over-contributed if you are going on Medicare in September. In that case, your math looks correct, and you will have to withdraw $1,400 from your HSA before the 2022 tax deadline. You will only get a deduction for the $3,100 of eligible contributions. The remaining $1,400 that you over-contributed and took back will have no tax impact, but any earnings received on that amount will also have to be withdrawn and will be taxable. If you withdraw it before December 31, 2022, it will go on your 2022 return.
If your current plan is an individual plan, your spouse will have to have some sort of high deductible health plan to make contributions to their HSA. Their contribution amount will be determined by whether or not it is self or family coverage.
