This would be incorrect: "You have to file Form 5498 to show to the IRS the amount of Rollover contribution"

Let's review:

A 1099-R is issued to the IRA Account owner by the brokerage or agency where the account resides and reflects money out activity for that year.

A 5498 is issued to the IRA Account owner by the brokerage or agency where the account resides and reflects money in activity for the year.

The tax payer issues neither form. The tax preparer issues neither form. The Tax Return will include form 8606 when specific circumstances apply.

This would be considered a rollover, and not an RMD, and as long as there was no withholding or you "put back" the same amount as was taken even if there was withholding, and met the other requirement(s), then that would be a nontaxable event.