From Treasury Decision 9324 IRS 2007-22 I.R.B. 1302:
Designated Roth Contributions as Excess Deferrals
Even though designated Roth contributions are not excluded from income when contributed, they are treated as elective deferrals for purposes of section 402(g). Thus, to the extent total elective deferrals for the year exceed the section 402(g) limit for the year, the excess amount can be distributed by April 15th of the year following the year of the excess without adverse tax consequences. However, if such excess deferrals are not distributed by April 15th of the year following the year of the excess, these final regulations, like the proposed regulations, provide that any distribution attributable to an excess deferral that is a designated Roth contribution is includible in gross income (with no exclusion from income for amounts attributable to basis under section 72) and is not eligible for rollover. These regulations provide that if there are any excess deferrals that are designated Roth contributions that are not corrected prior to April 15th of the year following the excess, the first amounts distributed from the designated Roth account are treated as distributions of excess deferrals and earnings until the full amount of those excess deferrals (and attributable earnings) are distributed.
What this says is that if you fail to obtain a distribution of this excess by April 15, 2022, the excess becomes pre-tax money in the Roth 401(k), taxable upon distribution (whether or not the distribution would otherwise be a qualified distribution). No matter when you take them, the first distributions that you take from the Roth 401(k) will be taxable distributions of this excess (and earnings attributable to the excess) until all of the excess and attributable earnings have been distributed. Because the attributable earnings must be distributed, failing to make the correction timely would create a real accounting mess. It's doubtful that the plan would be of any help in tracking the excess and the attributable earning, unless by notifying the plan they segregate the excess and attributable earnings into a separate subaccount.
Also see CFR 1.402A-1 Q&A-2(c): https://www.law.cornell.edu/cfr/text/26/1.402A-1
No, there is no provision in the tax code to treat the excess as part of a subsequent year's contribution.
