If you're not already familiar with the Armoury Exchange extension for Darktide, please see: https://www.reddit.com/r/DarkTide/comments/1000s5t/formally_announcing_the_armoury_exchange/
This is executable that will run locally and continuously scrape your Armoury Exchange results for matches. When matches are encountered, a new browser window will be launched, and you can also receive some alerts via another 3rd party service of LogSnag.
This has only been developed and tested on Windows, and works best with Firefox (Chrome is not quite behaving as expected).