Does my employer send a corrected 2020 W-2 for excess 401k contributions? They say a refund and 1099-R are sufficient. Will I be taxed/penalized for this without a W2?

[SaDe9123]

While working at 2 different companies in 2020, I contributed excess (about $2000) to my 401k. I informed one employer and the company managing that 401k. My employer says the 401k company will issue me a 1099-R form and refund, but my employer will not issue a corrected W-2. My understanding was since I caught the overcontribution before filing my 2020 taxes, my employer can correct my W-2. With a corrected W-2 my total retirement plan contributions between the 2 plans will not exceed the $19,500 limit, I won't be penalized for an early withdrawal from my 401k, and those contributions won't be taxed twice (between this and next year). Is this understanding correct? Should my employer issue a corrected W-2 or is a 1099-R sufficient? If the W2 is the better option, are they obligated to make the correction?

Additional information:
I made contributions to both a Roth and pre-tax 401k (about 30/70 split between plans respectively).
I'm below the eligibility ages for 401k withdrawal or catch-up contributions.

[macuser_22]

No.  You file the W-2 as it is.   You cannot correct a 2020 W-2 after December 31.  2020 is over and what happened cannot be changed.

You will receive a 2021 1099-R in Jan, 2022  that will have to go on an amended 2020 tax return to report it. 

It is not an early withdrawal, it is a return of contribution that was excluded from your 2020 income so yiu are not paying tax on it, and the 1099-R will add it back so it can be taxed.    Any earnings on the excess removed in 2021 will be reported on a separate 1099-R that goes on your 2021 tax return  next year.

For information see IRS Pub 525 page 10
https://www.irs.gov/pub/irs-pdf/p525.pdf