This seems like a good candidate for the cause of the problem:
I’m logged into the website on Chrome, so if it’s importing cookies from Chrome on launch, that would explain how I am already logged in on Edge. I tried logging out on Edge, then closing and reopening the browser: I was already logged in. Then I tried logging out on Chrome too. Now when I reopened Edge, I finally got the login screen. But the Import browser data on each launch setting mentioned in the article does not appear in my settings, so I can’t turn it off.
Edit: When I opened Edge manually, the setting did appear. I turned it off, and now the manual instance is going to the login screen. But this hasn’t fixed the problem in Katalon: if I’m logged in to the site in Chrome, then I am automatically logged in when I try to run a test in Edge Chromium. Can I change this browser setting somehow in Katalon?