Can we use turbotax easily if we sold and bought homes in different states?

Yes you can use TurboTax.

You do not "report" buying a home on your tax return.   All you enter about a house you purchased is mortgage interest paid, property tax paid or loan origination fees and private mortgage insurance.   Sounds like the only thing you might have for the new home is property tax if you paid it in 2021.

As for the house you sold:

SALE OF HOUSE

If your gain was more than  $250,000 filing Single, or more than $500,000 filing Married Filing Jointly the sale must be reported on your tax return.  Whether you re-invested the gain in to another house is irrelevant.  If you  have a Form 1099-S go to Federal>Wages and Income>Less Common Income>Sale of Home (gain or loss)

If you owned and lived in the home as your primary residence for at least 2 of the last 5 years on the date of the sale, you do not have to report the home sale if the gain is less than $250K filing Single, or less than $500K filing Married Filing Jointly (and you both owned and lived in the home for at least 2 years).

• If you are using online TT, you need Premier or Self-Employed software to report the 1099-S
• .https://ttlc.intuit.com/questions/1901135-i-sold-my-home-at-a-loss-is-this-deductible