If TurboTax is asking you to set a date to pay your federal taxes even though you have a state refund (or vice versa), it's because federal taxes cannot be deducted from your state refund or vice versa.
Reach back out if you meant something else.
If they are handled separately then why did it already deduct the federal taxes from my total refund amount?
The “summary” given to you by TurboTax must have confused you. That summary just nets out the difference between a refund you are getting and an amount you owe. Or it adds two refunds or tax “due” amounts together.
The federal and state treasuries are completely separate from each other.
Your state tax due cannot be paid from a federal refund.
And….your federal tax due cannot be paid from a state refund.
Neither refund can be used to pay the amount due to the other one.
If you owe tax due, you have to pay it yourself by the filing deadline on April 15, 2025.
If you have federal tax due you can pay by mailing your payment with the 1040V voucher, (which has the address printed on it, having the payment taken out of a designated bank account, or you can pay directly on the IRS website.
https://ttlc.intuit.com/community/tax-payments/help/how-can-i-pay-my-federal-taxes/00/26212
To apply for a payment plan with the IRS
Apply Online for a Payment Plan
You must pay your state tax due using the state’s preferred method of receiving payment. For most states that will be by making a payment to the state’s own tax website, or by mailing a check or money order.