For video, the field you want is Media Created, rather than Date Taken.

I wanted an easy approach that would support both pictures and videos, and didn't find one that I felt worked well for my purposes. So, I made a small utility program that would handle it. You can find it here at https://github.com/DanKonigsbach/GetItemDate

The trick was that rather than look at EXIF data, video metadata or shell folder attributes, I used the Windows shell properties API, which behind the scenes maps the various sources of that date into the field Item Date. Very convenient.

Less convenient for the C# and PowerShell developer is that this is an unmanaged Windows API. There might be a P/Invoke way to get at it, by for my purposes it was easier to just invoke a small utility executable.

Hopefully, either the source code or executable in GitHub will prove useful.