Deductions & credits

Actually, the Family limit is not $9,100. The Family limit of $7,100 is shared by both spouses and the $1,000 bonus is attributed only the the HSA whose owner is 55+.

That is, you cannot contribute more than $8,100 to any one HSA, because the other spouse $1,000 bonus must be contributed to that spouse's HSA.

"Is $9100 the limit on what they can contribute to plans or is that the limit of the net amount that can remain in their HSAs after qualified medical expenses have been paid."

The $8,100 plus $1,000 is the limit of what you can contribute. It does not matter how much is spent each year from the HSA(s) or if you spend nothing at all and have bundles of cash to carry over to next year.

"My wife and my HSA plans allow us to contribute an aggregate of $12650 and we have qualified expenses of over $5000 for a net contribution of $7650."

I don't understand what this means. It does not matter what your HSA plans say; the only thing that matters is what the IRS describes (not always clearly) what the rules are for calculating your individual annual HSA contribution limit.

"Since this net amount is less than the $9100, do I have any excess contributions?"

No, this is not how the annual HSA contribution limit is calculated. As I noted, the annual HSA contribution has nothing to do with how much you spend out of the HSA or how much you have left over.

The only thing that matters is how much you contribute in any given year.

Above, I said that you two could contribute $8,100 to one HSA and $1,000 to another. But to be clear, the $7,100 that is the Family coverage is shared and you two can split it any way you like.

So, you two could split the $7,100 evenly between you, so $1,000+$3,350 for you and the same for your spouse.

Whatever you do, at least $1,000 of the contribution limit must go to each HSA. Of course, you don't HAVE to contribute the whole amount, but if you do contribute the whole amount, you must put at least $1,000 in each HSA, and divide the rest anyway you like.