Remember that HSAs are individual accounts, there are no joint HSAs for spouses.
If your wife is covered by your family HDHP (and has no "other" coverage) then she can make contributions to an HSA in her own name up to the family limit, even if you can't make contributions in your name, and even if she is not the "owner" of the insurance. She just has to be covered. Assuming she can't contribute via payroll, she can contact any bank that offers HSAs and make direct contributions from after-tax money and then take a tax deduction.
The overall family limit for 2024 is $8300 plus $1000 is she is over age 55. Your limit for 2024 is 4/12th of $8300 plus $1000, or $2766 plus $333 = $3100. That means that for 2024, your wife can contribute up to $6534 (that's $1000 personal catch-up plus $8300 minus $2766 = $5534 of the family limit). 2024 contributions can be made up to April 15, 2025 as long as you let the bank know that is what you are doing so the contribution is allocated correctly.
Then for 2025, if you wife is covered by your family HDHP and does not have an FSA or other disqualifying "other coverage", she could contribute $9550 to an HSA in her own name, even though you can't contribute in your name.
