Why did my federal refund direct deposit but my state refund get mailed out?

That is a question only your state department of revenue can answer.

Yeah, I definitely asked. The answer I was given, however "we wouldn't know anything about that"

TurboTax does not get any information from the IRS or state after you file your tax return, so no one at TT would know why the state mailed you a check instead of making a direct deposit.   But---you received your refund---you are not waiting for months like many others.