You are correct that both distributions will be reported in 2024. In January you will receive a Form 1099-R showing the total amount that you received in 2024, for both RMDs. Just enter the 1099-R as you normally would. It will not "mess up" your 2024 tax, but you will pay more tax because you are reporting double the amount of income from the annuity. There is nothing you can do about that.
You probably should have reported the missed RMD on Form 5329 in your 2023 tax return to avoid a penalty for not taking the RMD in 2023. You can file a 2023 Form 5329 now, by itself, not attached to any tax return. You do not have to amend your 2023 tax return.
2023 Form 5329
2023 Instructions for Form 5329
@dmertz - Any further comment or corrections?
