A couple of adjustments could be made to improve accessibility (a11y):
The search input in the dropdown needs to have a label and or aria tags (even if not visible)
The dropdown header (sm-header) should probably not be an H3, best to use a class instead, since modifying the template is not an option for that item. Have an H3 causes conflicts with the rest of the document hierarchy.
A couple of adjustments could be made to improve accessibility (a11y):
I am using the WAVE tool for A11Y https://wave.webaim.org/