You will benefit from filing separately. The IRS says if your modified adjusted gross income (AGI) is less than $150,000, then you can exclude up to $10,200 of unemployment compensation paid in 2020, or up to $10,200 per individual if married.
The $150,000 threshold appears to apply to any filing status according to the latest information from the IRS, so you would be able to exclude both your unemployment benefits by filing separately, but nothing by filing together.
You must amend by April 15 to go from joint to separate. The IRS says, "After the due date of your return, you and your spouse can’t file separate returns if you previously filed a joint return."
