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.
Hmm, you might be right, but I installed an APK recently (also on Lineage) and it asked me to authorize Firefox, it had the Firefox logo and seemed to suggest that future installs would be authorized. I cancelled it and opened it through the file manager.
