Although sometimes used, normalcy is less common than normality in American English. It is very rarely used in the UK, Canada, Australia, and New Zealand. It is frequent in India and Zimbabwe however.
So it’s a regional thing.
Although the claim that in US English the “normality” form is more common does not match my experience as a speaker of US English.
I believe Normalcy was pioneered as a word in a presidential speech by Warren Harding in 1920. The titular "Return to Normalcy". Before that, it was only normality. Since then normalcy has overtaken normality to become the more common word to use.