They would not get the Wage index increase for 2022. Directly from the page you cite:
"An individual's earnings are always indexed to the average wage level two years prior to the year of first eligibility. Thus, for a person retiring at age 62 in 2023, the person's earnings would be indexed to the average wage index for 2021"
And they don't get the COLA as that would be in the year they reach 62, the COLA increase calculated 3rd Q 2023. The definition of a donut hole.
Spouse just got off the phone with the Social Security about her new application as she turns 62 in January 2023. The representative told her the increase will be shown in her first benefits calculation notice sent within 30 days of application. Should be here in about 10 days, I will post those results when I get em.