I have had this very same question, from my (husband's) point of view. I like how you express the question, very simple and straightforward. I've actually done a lot of research on this over several years. And I believe I have the correct answer, although the documentation at the SSA is a bit lacking.
(if my discussion below is too long-winded, which it may be!) see this Ask Larry article that addresses this very question. Larry Kotlikoff is a university professor and expert on Social Security. See https://maximizemysocialsecurity.com/if-my-wife-takes-spousal-benefits-early-will-reduction-age-carr...)
My concern was for my wife. I took delayed benefits at age 70 and and we plan for my wife to take her spousal benefit at 62. Her FRA is 67, consequently her spousal benefit will be reduced accordingly. My question was what happens if I die before she reaches her FRA...does the reduction factor for her spousal benefit apply as well to the survivor benefit? or is the reduction based on her age at my time of death? And what if I live to after she's at her FRA, is there any reduction then?
It seems that the rules are different for taking benefits as a spouse and on one's own account, and for survivors benefit. For survivors benefit any reduction for age below FRA is based on the survivors age at the death of the primary beneficiary. Rules are different when someone is entitled to their own benefit and a spousal benefit. This latter situation was discussed recently on the forum here https://community.aarp.org/t5/Social-Security/Age-for-determining-spousal-benefit/td-p/2482544.
SSA document, POMS RS 00207.005 Widow(er)'s Benefits - Conversion of Benefits - Policy (https://secure.ssa.gov/poms.nsf/lnx/0300207005), addresses "Spouse to Widow's Benefit" in the third bullet point under point "C" and states "Age 62 through the month before FRA when the NH dies. An application is not necessary. If the spouse is also entitled to a retirement insurance benefit (RIB) or disability insurance benefit (DIB), a Certificate of Election (SSA-4111) is required to receive reduced benefits. Pending receipt of the certificate, the spouse is converted and placed in suspense (S-9) status so that he/she can be identified at FRA. If the widow(er) does not elect reduced benefits, he/she will be identified at FRA and awarded benefits." [NH is the Number Holder...the primary beneficiary...who just died]
So in some cases your spousal benefit will automatically changed to the survivor benefit, though there are some exceptions where you can delay the survivor benefit.
If your husband had any delayed retirement credits you will be entitled to those as well. But if your husband dies before your FRA and you end up taking the survivor benefit there will be some reduction in your benefit, it will not be exactly 100% of what your husband was receiving (including the delayed retirement credits).
I have found verification that any reduction for age for the survivor benefit is based on the age of the survivor at the NH's death in a number of places where it is implied but I've never found this explicitly stated in a SSA document. Hence my letter to Larry.