Does my wife need to wait until her full retirement age to receive her 50% spousal benefit?
Yes, unless she has a child in her care who is eligible for child's benefits and who is either under age 16 or is disabled. Otherwise, your wife's spousal rate would be reduced for age if she starts drawing prior to full retirement age (FRA).
If a person is eligible for just spousal benefits only and they file for benefits at their FRA or later, their benefit rate would be equal to 50% of their spouse's primary insurance amount (PIA). A person's PIA is equal to the amount of their Social Security retirement benefit if they start drawing at FRA.