I can’t find such a study, and it seems extremely unlikely to me that any such study was performed recently. The original law was passed in 2007, and then the regulations were in political limbo for more than a decade.

My base hypotheses here, subject to easy refutation by any real evidence, are that:

• The DOE has looked at no study from after 2007 to justify their current policies.
• This regulation is going into effect now simply because it was on the list of stuff Trump did that the Biden admin reversed.
• The effect on consumer electricity costs and carbon emissions are negligible, since LED bulbs are a decade cheaper and better and almost everyone voluntarily buys them.