Yes, you'd use the Self Employed Online version (or the TurboTax Home & Business Desktop version) to prepare your Forms 1099-NEC. You'll be directed to TurboTax Quick Employer Forms, where you'll follow instructions for preparation and printing.
If you e-file your forms using QEF, you don't need to file Form 1096 at all. I'm linking you to instructions on how to prepare your forms for contractors (or W-2s for employees) below.
How do I create W-2 and 1099 Forms in TurboTax?
I'm also linking you to a FAQ page for Quick Employer Forms. It's a great source of info for anyone using the program. You'll see your question about filing Form 1096 answered near the bottom of the list.
Quick Employer Forms | Common Questions (FAQ) (intuit.com)
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*** I am NOT a tax expert. I am a seasoned TurboTax user, and volunteer to provide assistance to TT users. Nothing I post is to be considered TAX ADVICE; I bear no legal liability for responses.***
