The rep at ETrade was apparently confused as to what you were trying to do. What you are trying to do is complete a late rollover under IRS Rev. Proc. 2020-46 self-certification that you would qualify for a waiver of the 60-day rollover deadline. This is not a regular contribution that would be subject to any contribution limit, not a contribution for 2023. It's a rollover. It's up to ETrade to accept or deny your self-certification. Because self-certification requires you to provide a written self-certification to ETrade as described in the Rev. Proc., it's doubtful that this could be done online.
https://www.irs.gov/pub/irs-drop/rp-20-46.pdf
If ETrade accepts the self-certification and allows you to complete the rollover in 2024, the 2024 Form 5498 from the IRA will show the amount in box 2 as a rollover contribution but will also report the amount in box 13a with code SC in box 13c. Given that more than one late rollover is involved, you would likely need to submit a separate self-certification for each rollover and I'm not sure how they would complete box 13b of the Form 5498 since distributions from multiple years are involved.
If ETrade denies acceptance of the self-certification, you could try another IRA custodian.
