"Do I include this recontribution done in 2023, even though it was done after April 15th 2023?"
Yes. From the instructions for Form 8915-F:
Include on this year's Form 8915-F any repayments you made before filing this year's return. Any repayments you made will reduce the amount of qualified disaster distributions reported on this year's return. Do not include on this year's Form 8915-F any repayments you made later than the due date (including extensions) for filing this year's return.
In this case, "this year's tax return" is your 2022 tax return.
