That's a weird one. @dmertz
Normally, an "indirect rollover" is perfectly fine. You take the money out of the 401k, deposit it to your checking account, then send a check or electronic deposit to the new IRA. You have 60 days to do this, and you can only do this once per year. (You can make more than one "direct" bank-to-bank rollover per year, but only one time per year where the money goes through your account.)
However in this case, you did the second step before the first step.
I have asked an expert to comment.
I have two comments myself.
First, if you ask the 401k to send you money as a rollover, they might send the check as "John Smith in trust for John Smith's IRA". If that's how the check is labeled, you can only send it to the IRA, you can't cash it. So you are stuck with too much money in the account.
My second comment is that, I think you can contact the new Roth IRA, say "it was all a mistake", withdraw the mistaken contribution, and close the account. You will also have to withdraw any earnings, and those earnings will be taxable on your 2024 tax return. Then, you can go back to bank #2, open another new Roth IRA, and do the direct transfer correctly this time.
I don't know if you can withdraw the money from the 401k after making the deposit to the new Roth and call it a rollover. I think you can fix this situation, but not in that manner. I think the order of events has to be different.
