I bought a house in 2021, and the seller rented back the house for 45 days. They paid the cost of my mortgage for that time period. How and where do I report this?

Based on the information your provided, the payment you received from the seller can be fairly characterized as Other Income.  To report this income, go to the Wages & Income section (you will need to click the Federal Taxes tab first).  When you are in the Wages & Income section, scroll down to the bottom of the page where you will see Less Common Income, and at the bottom of that list, select Miscellaneous Income.  

On the next page, select Other Income and respond accordingly to the questions.  You will have to enter the amount you received, and a short description of the income.  When done, this income item will be on your Form 1040, line 8.  

If you are using TurboTax Online, here are the steps to follow to preview your Form 1040:

       Open or continue your return.

1. Select Tax Tools in the left menu (if you don't see this, select the menu icon in the upper-left corner).
2. With the Tax Tools menu open;
3. Select Tools.
4. Next, select View Tax Summary in the pop-up.
5. Then Preview my 1040 in the left menu.

Last time I saw this question was over 3 years ago, and apparently I "found" something and was able to answer it. However, I failed to document what I found, or where I found it. So here's a link to the reply I provided a few years back. Basically, you'll either report it as "other income", and/or reduce your cost basis in the property by the total income received under the leaseback. No SCH E is needed and no depreciation needs to be taken since the leaseback was for less than a year.

https://ttlc.intuit.com/community/taxes/discussion/okay-i-found-it-but-based-on-information-in-multiple-pla/01/596995#M242578