I filed an amended return for 2023 on May 14, 2024. It was accepted and entails a refund. When do you think it might be paid?

Do not expect quick results from amending. It can take four months or more for the IRS to process an amended return.  

You can watch for information here:

https://www.irs.gov/Filing/Individuals/Amended-Returns-(Form-1040-X)/Wheres-My-Amended-Return-1

Per the IRS, a federal amended tax return can take up to 20 weeks to process and maybe longer.

Go to this IRS website for the status of an amended federal tax return, form 1040-X - https://www.irs.gov/filing/wheres-my-amended-return