We figured it out. It is because our app is a browser app.
Apps that have the com.apple.developer.web-browser managed entitlement may not claim to respond to Universal Links for specific domains. The system will ignore any such claims. Apps with the entitlement can still open Universal Links to other apps as usual.
From https://developer.apple.com/documentation/xcode/preparing-your-app-to-be-the-default-browser
It would be great to link this information in the Universal Link debugging so that it is an easy check for folks! I had to dig through the logs to determine it could be an issue with the fact that this was a browser app.
Topic:
App & System Services
SubTopic:
General
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