I thought I opted for Turbo Tax to send my state taxes owed on a date. I can't see that it's been taken out of my account and I can't find where to manage or check on it.

[SteamTrain]

Get your tax file PDF and look the state "Electronic Filing Instructions"

IF...if, you arranged the payment with your efile, that worksheet will look like the following.....check the dates and account numbers too.

TurboTax doesn't do it...TTX just includes the information with your tax e-file and the state does the debit.

Of course, if your state tax E-file is rejected...then nothing happens until you fix the E-file problem and get it  successfully accepted.