@kim_hung_lo
For 2025, you are correct. $1000 catch-up must go into her account, $1000 into yours and the $8550 can be split any way you like.
I also want to double-check about 2024. What insurance do you have now? If it is a family HDHP, then the same rules apply. Using the last month rule, either you or your wife can split the $8300 limit for 2024, plus $1000 each individually. Your wife is "covered" by a family HDHP for HSA purposes if you have a family HDHP (maybe for children), even if your wife is not officially covered.
If you only have single HDHP for 2024, then you can contribute $4150 plus $1000, and your wife can't contribute anything.
However, I also want to point out that loss of a job is a "life event" that should allow you to enroll your wife on your company plan right away, without waiting for the open enrollment period. If you can switch your coverage from single to family on or before December 1, 2024, you can use the last month rule to contribute up to $8300 plus $1000 plus $1000, even though she will only have been covered for one month. You can make tax deductible contributions retroactive to 2024, as late as April 15, 2025 and take the tax deduction on your return.
