I have installed GNOME Shell extensions from two sources:
Sometimes I get prompted with an upgrade from extensions.gnome.org, but I can't tell what the original state of the extension was (so I can decide whether to get the upgrade, switch source, etc).
How can I see which source an extension came from?
The prompt to upgrade is coming from your browser's "GNOME Shell integration" plugin. If you follow the prompt you will be taken to https://extensions.gnome.org/local/ where all your extensions (from both sources) will be listed.
Extensions from the website have a red "X" button, indicating they can be uninstalled. Local packages cannot be uninstalled by "GNOME Shell integration", so they don't get an X.
In Debian-based distributions, most extensions are found in individual packages gnome-shell-extension-X or gnome-shell-extensions-X. Other distributions may follow a similar convention.
The exception is the package gnome-shell-extensions (no suffix). This package contains the set of "official" extensions from GNOME. These are likely the ones installed as local packages.