I have a MacBook Pro 13" Mid 2012 with High Sierra 10.13.6. Do I need to upgrade my office 2011 before or after I upgrade from 10.13 to Catalina 10.15 or Mojave 10.14?

If you upgrade to Mojave, no.

If you upgrade to Catalina, you'll need to upgrade Microsoft Office or use a product such as LibreOffice instead.

(214910)

The current version of Office installs only under macOS 10.15 Catalina, macOS 11 Big Sur, and macOS 12 Monterey:

MS Source link: https://support.microsoft.com/en-us/office/office-2019-for-windows-and-mac-faq-a8fed43d-4c11-404a-acc3-09eb46a3a7fb

Scroll down to "Support and System Requirements for Mac" and look at the second item in that section. This is it:

It appears you need to be at Catalina to install Office 2019.