I’m filing in 2025 for my 2024 return but the IRS claims my accepted API on the 2023 return does not match what they have on record even though it should?
I assume you mean AGI (adjusted gross income.) And I'll assume this is a filing status of single, since you didn't say otherwise.
If you used the 2023 AGI from the original 2023 return (not an amended one) Form 1040, Line 11, and if it was rejected, then try to use a 0 (zero) for the 2023 AGI and efile again.
For some reason it's not matching the IRS database. This is more prone to happen if one filed the 2023 return late in the year, but sometimes there's not a known reason.
ADDENDUM:
In addition to the information above, if you owe Federal taxes due, be aware that time is growing short to get this issue worked out before additional penalties.
If you are due a Federal refund, there is not a penalty for a late Federal return. On the other hand, if you owe Federal taxes due, you could end up with both a late filing penalty and a failure-to-pay penalty if it continues to reject and you go past the date to timely postmark a paper return. The IRS says:
"To timely file a paper return after an electronic return was rejected, your paper return must be postmarked by the later of the due date of the return (including extensions) or 10 calendar days after the date the IRS gives notification that it has rejected your electronic return."