Point README Binder links to the version-pinned binder-stable branch (#237)

* Point README Binder links to binder-stable

* Apply suggestion from @krassowski

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Co-authored-by: Michał Krassowski <5832902+krassowski@users.noreply.github.com>

Author: MUFFANUJ

README.md

@@ -7,9 +7,11 @@
 
 | Try in your browser   | Lab                                                                                                                                                       | Notebook v7                                                                                                                                                            |
 | --------------------- | --------------------------------------------------------------------------------------------------------------------------------------------------------- | ---------------------------------------------------------------------------------------------------------------------------------------------------------------------- |
-| Binder (Powerful)     | [![Binder](https://mybinder.org/badge_logo.svg)](https://mybinder.org/v2/gh/jupyterlab/plugin-playground/main?urlpath=lab)                                | [![Binder Notebook v7](https://mybinder.org/badge_logo.svg)](https://mybinder.org/v2/gh/jupyterlab/plugin-playground/main?urlpath=tree)                                |
+| Binder (Powerful)     | [![Binder](https://mybinder.org/badge_logo.svg)](https://mybinder.org/v2/gh/jupyterlab/plugin-playground/binder-stable?urlpath=lab)                       | [![Binder Notebook v7](https://mybinder.org/badge_logo.svg)](https://mybinder.org/v2/gh/jupyterlab/plugin-playground/binder-stable?urlpath=tree)                       |
 | JupyterLite (Instant) | [![JupyterLite](https://jupyterlite.rtfd.io/en/latest/_static/badge-launch.svg)](https://jupyterlab-plugin-playground.readthedocs.io/en/latest/lite/lab/) | [![JupyterLite Notebook v7](https://jupyterlite.rtfd.io/en/latest/_static/badge-launch.svg)](https://jupyterlab-plugin-playground.readthedocs.io/en/latest/lite/tree/) |
 
+<!-- Binder links above are intentionally pointed at the `binder-stable` branch with pinned Binder dependencies; update that branch only after validating Binder builds. -->
+
 A JupyterLab extension to write and load simple JupyterLab plugins inside JupyterLab.
 
 ## Install