If you selected to pay the federal taxes owed using direct debit from your bank account, that information was sent with the e-filed return. The IRS will debit your account on or after the date you selected to have the taxes paid.
Your proof of payment is on your bank statement.
Check your IRS tax account for payments made - https://www.irs.gov/payments/your-online-account
What do you mean by initial payment? When you pay through the TurboTax system you must pay the entire balance due in full in one payment. It cannot be a partial payment. Do you think you were paying one quarter of the taxes that were due? If so you weren't paying attention to the forms, there was one payment voucher for the entire 22 balance due and then for estimated tax payments for the 2023 tax year. That first estimated payment was not for the 22 balance due.
There is an option, at the end when you select payment, to set up a payment plan, and when I chose that option, TurboTax sent me to the IRS website. On that website, there are multiple options for selecting a payment plan.
IRS will tell you if your payment plan is approved.
You will be paying interest.
TurboTax is not informed of any arrangements you have made.