You can treat that period as a second home.
You still qualify for the home sale exclusion because you owned and used your home as your main home for a period aggregating at least two years out of the five years prior to its date of sale. Topic No. 701 Sale of Your Home
You did not charge any rent so your home was not a rental property.
The IRS allows you to deduct mortgage interest and property taxes on two homes so you can claim the interest and taxes on both homes on your 2020 return.
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