I don’t think there’s an easy solution for this. We don’t have an interface that provides this access, and I don’t think anyone is working on writing one.
On the safety side, the D-Bus interface only allows installation of extensions made available on extensions.gnome.org, which in turn need to pass their review guidelines. So it’d require a review failure there to turn this into a sandbox escape.
You would have access if running with classic confinement, but it’s not clear it would pass the classic confinement review guidelines as “3rd party installer snaps” are explicitly listed as unsupported.