IRS Publication 970, page 54 says
"Don't report qualifying rollovers (those that meet the above criteria) anywhere on Form 1040, 1040-SR, or 1040-NR. These aren't taxable distributions." When it refers to the above criteria, one of the rollover types is the transfer to a Roth IRA as long as it meets all of the criteria (explained on page 53 of pub 970).
From past experience with 529 plans and the IRS, I am not convinced they won't routinely consider this unreported income that you have to explain. But their publications support the idea that none of this gets reported. I just hope that when this is reported to the IRS by the institutions, that the IRS understands what they are seeing.
