"My wife was not employed" - does not matter
"and she was under MY HDHP family plan for entire 2021." - this is what matters, that she had Family HDHP coverage, period.
"Is the applicable HSA contribution limit for us" - not US, just your spouse. Your annual HSA contribution limit for 2021 was zero because you were on Medicare the entire year. Your spouse, on the other hand, has the limit of 7,200 for 2021 because she was under the HDHP for all 12 months (it does not matter when she opened the HSA).
"TT regarded the entire contribution to my HSA in 2021 ($3,750) as "Other Income or Loss." I thought as long as the sum of "my contribution to my HSA" and "my wife's contribution to her HSA" is less than the limit ($5,400), it is nontaxable. Is my understanding wrong?" No, it does not work that way. The HSA is owned by the individual. The annual limit is for the individual HSA. The shared Family limit can be shared ONLY if both spouses are eligible, but you were not. As a result, your spouse gets it all.
So while you could not contribute anything to your HSA, your spouse could contribute the annual Family maximum to hers.
The Family annual limit is shared between the spouses (if they are both eligible), but the actual limit is per HSA.
Your wife has until April 18th to contribute to her HSA retroactively (i.e., for 2021). Since she has contributed only $25 so far, she can contribute the other 7,175 to her HSA by April 18th - but she must make sure that the HSA custodian knows that it is for 2021 and not 2022.
Make sense?
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