How theme exposed form of date field with BETWEEN operator?

Problem/Motivation

I want to customize the display of the date filter field when the operator BETWEEN is selected, but unfortunately I can't find how to do it.
At first I thought that using this file, you can redefine the template of the expanded Views filter
https://git.drupalcode.org/project/date/-/blob/7.x-2.x/date_views/theme/...
but technically it does not look like what Views renders

Please tell me if you can somehow redefine the filter output template, I want to wrap it in Bootstrap classes, so that the Start date field is in the first column, and End date is in the second column