Unless you do a correct 1031 exchange using a third party administrator so you don't touch the proceeds of the sale then you cannot avoid paying taxes on the sale of rental in the year it is sold no matter what you do with the proceeds.
And if you have not been properly depreciating the rental you need to RUN to a local tax pro to correct the error on the 2021 return.
Now if you do complete a 1031 exchange and move the old basis to the new property in a timely manner then you may be able to move into the home and later use the personal residence exclusion.
Go to this IRS website for section 1031 like kind exchanges - https://www.irs.gov/businesses/small-businesses-self-employed/like-kind-exchanges-real-estate-tax-ti...
Also see this website for like-kind exchange rules - https://www.investopedia.com/financial-edge/0110/10-things-to-know-about-1031-exchanges.aspx
