The Short Version
This claim is false. The "once every 823 years" figure is a recycled internet hoax. Every non-leap-year February has exactly 28 days, meaning it always contains exactly four of each weekday — that's basic math, not a miracle. The specific "perfect February" layout where February 1 falls on a Sunday last occurred in 2015 and will happen again in 2037. The Gregorian calendar repeats on a 400-year cycle, making an 823-year uniqueness claim mathematically impossible.