What do i do to correct the issue where my federal tax payment was taken twice out of my checking account and I have now paid twice what I owed?

You will have to contact the IRS and speak with an agent concerning double payment.

Call the IRS: 1-800-829-1040 hours 7 AM - 7 PM local time Monday-Friday
When calling the IRS do NOT choose the first option re: "Refund", or it will send you to an automated phone line.
So after first choosing your language, then do NOT choose Option 1 (refund info). Choose option 2 for "personal income tax" instead.
Then press 1 for "form, tax history, or payment".
Then press 3 "for all other questions."
Then press 2 "for all other questions."
- When it asks you to enter your SSN or EIN to access your account information, don't enter anything.
- After it asks twice, you will get another menu.

Press 2 for personal or individual tax questions.
Then press 3 for all other inquiries
It should then transfer you to an agent.

Discussions from 2022 and earlier indicated that you could call the IRS as described here, but if you do nothing they will eventually issue you a refund when they process your return. Is this still the case?

Yes, in most cases, the IRS will refund the payment.  @ngerard221 

The keypad sequence above no longer works beacuse IRS has changed the menu.

The same thing happened to me. The IRS phone menu has changed. Here is the new way:

Call 1-800-829-1040. They say, "Tell us in a few words why you are calling."

     Answer "Personal income tax"

They say, "What type of income are you calling about?"

     Answer: Press 1.

After a hold, you get an agent. They verify they have received both payments and issue a refund, saying it will take 4-6 weeks.