for the full exclusion the 2 rules are one or both of you must have owned the property for 2 out of 5 years before the sale and both must have occupied the residence as their principal residence for 2 out of 5 years before the sale. the periods of occupancy as their primary residence does not need to be the same.
so, for your spouse occupying it as her principal residence from 11/30/17 to 7/31/2020 would mean she meets the 2-year occupancy test. you occupied it from 11/30/17 to 8/31/2019 or 21 months/639 days (you use either full months or nights)
you are going to have to make the call on whether you were occupying the house as your principal residence.
however, the way an IRS agent would look at these dates is - where is your job? where are you registered to vote? where are your vehicles registered? No one is conclusive but to job location is a major item and likely these days would not be included.
Between September 1, 2019 and August 1 2020, I returned to live in the house for at least 28 days. 11 days in March, 2020, 12 days in May 2020 and 5 days in October 2019.
so, your wife gets the full $250K exclusion. since you had a job change you are probably entitled to a partial exclusion equal to days use as principal residence divided by 730 times $250,000
also, extremely important, before any home sale exclusion applies you must recapture the depreciation allowed or allowable during the rental period.
