I've posted this question in the Slack community and another user has also reported the same problem. Other than that, I couldn't get much discussion going on over there. Here's what's happening:
I follow the link from the iOS Gmail app to open in iOS Google Chrome. The browser prompts "This page will open in another application." I tap "Open" and the page reloads in the browser and shows the prompt again. I tap "Open" again before finally being taken to the app store to install my app for the first time. (See attached video) If I don't tap Open quickly and instead wait for a bit to do so, the prompt closes and nothing else happens. Meanwhile the fallback link has loaded in the background and that's all I see. I only experience this in iOS Chrome, not Safari nor Android Chrome. Is this something others here are seeing? Is the Firebase team aware of it, so they can communicate it to the Chrome team?