The payroll system withholds taxes based on the information on the State and federal W-4 forms along with instructions regarding where the work was done. You don't need a new W-2 unless a number is wrong. The state numbers are based on the W-4 that was active for each paycheck. They are not wrong. The final forms you submit will allocate the funds based on the final reality.
The state income tax forms will want to see how the money that is on the federal lines is split. The numbers on the state line show what was withheld, and the gross income that was used to calculate that withholding.
Your situation isn't any different than a employee who forgets to tell the payroll department that they moved from state A to State B, which in some cases changes the amount of state taxes and where they are sent. They don't get a new/corrected W-2 because none of the numbers have to change.
You will have to redo your state tax forms to reflect the months you didn't have Vermont income. You will use your original W-2.
Because of COVID work issues states are having to address this.
Vermont has done so: Guidance for Remote or Relocated Workers Due to the COVID-19 Pandemic
During “normal” times, I live in (am domiciled in) New Hampshire and
drive to Vermont every day for work. Since the beginning of the state
of emergency, I am working at my Vermont job remotely from my home in
New Hampshire. Do I still need to pay Vermont Income Tax?
Prior to the pandemic, you were required to pay Vermont income tax as
a nonresident on the income earned in Vermont. Presently, however,
given your New Hampshire domicile and your remote worker status, the
income you earn while at home is not Vermont income (even though your
employer is still located in Vermont) and is not subject to Vermont
Regarding which form to use:
Nonresidents with a filing requirement will file Form IN-111, Vermont
Income Tax Return and Schedule IN-113, Income Adjustment Calculations.