JS Packages: Explore separate build for `stores`

This is the follow-up for https://github.com/Automattic/jetpack/issues/35076.

Per @anomiex suggestion:
>The next step towards the stores being a separate thing would be to build them as a separate bundle, that has a separate wp_register_script() call registering it, and then everything needing it depends on that bundle (maybe via some custom configuration on @wordpress/dependency-extraction-webpack-plugin)?

> We'd probably want to put the separate bundle and the wp_register_script() call into a composer package. Possibly automattic/jetpack-assets if we don't want to create a new one just for it, although a new one would probably be cleaner.