The Acrobat Reader mobile app is not an in-app file browser, nor a web browser of any kind. As such, it doesn't have the ability to select from the app itself which web browser should be used as default when opening PDF files.
That is handled at the iOS level of your mobile device.
The Acrobat Reader is PDF viewer that when you sign in with your AdibeID (if you have a paid subscription of Adobe Acrobat, for example), it also unlocks some premium PDF editing features.
In addition, it also integrates cloud services with different providers.
That is, by far, nothing as an "in-app browser". In its own right, the Acrobat Reader mobile app is a native PDF handler and PDF viewer.
However, I think the topic could get confusing because most Apple users want to do everything through their iOS or macOS integrated web browsers, to include the ability to edit, and fill and sign PDFs.
Sorry for the long verbage, but I think all you have to do is set the Safari browser in your iOS device as the default PDF handler, not the Acrobat Reader mobile app.