Could a Unity app running on Android install another APK on the device from the web?

After downloading an APK file to the device from the web, with the right permissions, could it be installed from the unity application?

The Split APK is designed for this purpose.

The initial file is supposed to be <50mb and it is intended to be a setup file for downloading the extra APK (<2GB) from the web/Play.

Check Google developer Documentation.

For an APK to install an external APK, there may be a snag.

Note that most devices come with “Allow External APKs” disabled by default so such “Sideloading” may not be permitted.