I don't think this is how it works, at least not from my past experience with Lineage. A browser isn't an app installer, as when you download an APK from it, the APK is staged through the phone's integrated file manager (aka "Downloads" app), and is treated as having no real source.
As far as I know, real "app installers" are purpose-built programs such as Amazon Appstore and F-Droid.