So, your father, as a separate legal entity, files a 2023 return for all income received up to the date of his death. That's the last responsibility your father has.
The estate is a separate legal entity that handles income received after the date of his death, and the estate does need a separate tax number. The estate should handle all his income after death, even if it is reported with his SSN (the IRS knows that the SSN and TIN are linked).
However, you can't prepare an estate tax return (form 1041) using the normal version of Turbotax. You need Turbotax Business (for corporations and estates) (this is not the same as "Home & Business"). There is an online version and a version you can buy to install on your own computer.
It looks like you need to file if the estate has more than $600 of income, but I'm not sure about that.
https://www.irs.gov/individuals/file-an-estate-tax-income-tax-return
If you try the online program, you probably don't pay until you file, so you have a chance to enter your info and see if a return is actually required.
https://turbotax.intuit.com/small-business-taxes/cd-download/
