It seems that the “Launch URI” feature is not working for certain domains in the iOS app. Specifically, the button does not appear for .eu domains. However, when changing the domain from example.eu to example.com, the feature works as expected. Interestingly, the issue doesn’t affect the macOS desktop client or vault.bitwarden.com.
PS: I had to merge the images into one because the site wouldn’t let me upload three separate images as a new user.