You both were still married on December 31. You need to file as MFS Married Filing Separate or Head of Household if you qualify. If she qualifies as Head of Household that's ok. She doesn't have to be Single to file as Head of Household.
But if she filed as Head of Household and Itemized Deductions you also have to Itemize even if it is less that the Standard Deduction. If she took the Standard Deduction you can do either way, Standard or Itemized Deductions.
Here's a FAQ for Head of Household
Can a married person file Head of Household?
she may have been entitled to file as HOH
a married taxpayer who is a US citizen or resident can file as HOH IRC sec 7703(b) if all the following tests are met
1) she files her own return
2) she paid more than 1/2 the cost of keeping up their home for the year
3) she lived apart from you for the last 6 months of 2019
4) her home was the main home for more than half the year of her child, stepchild, adopted child or foster child. the child must be a dependent or would be a dependent except that she released the exemption to you - the noncustodial parent
then all you can do is file as single
if there's a failed test all you can do is file as married filing separate - you can not force her to file a joint return. note if she itemized so must you or if she took standard so must you.