Estimated Payment for 2023 incorrectly assigned to 2022

Hello and thank you for reading and any help you can give.

I use EFTPS to schedule my estimated tax payments. While setting up my 2023 tax payments I incorrectly entered the year on one of them and mistakenly assigned it to 2022.

 

Seeing this was incorrect, the IRS sent me a refund check with interest. I called them, and the IRS agent I spoke with told me to return it to the Refund Inquiry Unit, explain what happened, and request that the amount be applied to my 2023 taxes.

 

I followed the instructions. I'm waiting to hear back from Refund Inquiry.

 

My question is this: I'd like to finish and file my 2023 taxes next week. Should I assume that the Refund Inquiry Unit will properly apply my payment and report it as estimated taxes paid, or should I report the amount as not having been paid and pay any "uncovered" taxes, or is there another option? Regarding refund, I expect to get one, but I don't yet have an estimate of its size.