So would the 28 days that I spent in the house after September 1 2019 count towards the total?
That's your call, and you'd have to prove it if audited. For example, if you owned/rented another house during that time period, you can only have one primary residence at a time. So if you claimed a "home exemption" on property taxes (if offered such an option on property taxes) for the entire tax year on another home, then the first home could not be claimed as a primary residence when occupied at any time the 2nd home was being claimed as your primary home for the property tax exemption stuff.
Note also that if you do not qualify for the full exemption, you "May" qualify for a partial exemption. Read IRS Publication 523 at https://www.irs.gov/pub/irs-pdf/p523.pdf starting on page 6, under "Does your home qualify for a partial exclusion of gain?"
