If you have a Federal extension, your NJ extension is automatic also.

You don't have to include any Form with your e-Filing.

Nor can you do that.

PS anybody can get form 4868 right now from IRS website and put their name on it, so including it now  is meaningless.

When e-Filing,

"fill in the oval (regarding extension) on the front of your NJ-1040."

Presumably, TurboTax will handle this for you since it knows you requested a federal extension.

I did fill in the oval on the NJ return.  I hope you are right about TT providing the info, but I have my doubts.  Looking at the NJ tax web site they require a Fed confirmation number for online filing, a copy of the Fed  paper extension form 4868 that was filed May 17, 2021  or the NJ -630 extension mailed on May 17, 2021.   https://www.state.nj.us/treasury/taxation/questions/extension.shtml

it says,

if filed by paper,

that means if you filed the 4868 on paper, and, you are filing your NJ return on paper.

see IRS website to file a request for extension online, no paper required.

If you print a paper copy of NJ for your records,

you should see, on Page 1, a mark next to the line "Federal extension filed."

Always print a copy of your completed tax return(s) for your records, and review it carefully before e-Filing.
You will need it if you are audited by the IRS, or to amend if a TurboTax update changes your return or for any other reason,

AND, to find your AGI next year.