Plugin registration issue between file browser and github browser

## Description

Notebook widgets from Launcher gives "Repository is read only" error after installing jupyterlab-github in JuptyerHub with JupyterLab > ver.4+. It tries to open Untitled.ipynb inside GitHub Browser instead of default File Browser pane.

A workaround is to select any file in the File Browser (no need to open it) before clicking the notebook widgets.

## Reproduce

1. Launch JupyterHub (docker run -p 8888:8888 quay.io/jupyter/datascience-notebook:hub-4.1.5)
2. pip install jupyterlab-github
3. Refresh browser
4. Click on any Notebook widgets from Launcher

## Expected behavior

The new file Untitled.ipynb should open in File Browser pane instead of GitHub browser pane, which is read-only.

## Context

- Operating System and version: Ubuntu 20.04.6
- Browser and version: Firefox 115 / Edge 128 / Chrome 127
- JupyterLab version: 4.2.0
- JupyterHub version: 4.1.5