For bigger teams, we recommend to look into more sophisticated Figma theming plugins. The most common approach right now is to use Tokens Studio, which lets you import the themes data from the style libraries and store themes using an external storage. It means that all your team members will be able to fetch the tokens from a single storage and automatically receive updates in the future.
For the best experience of working with themes, we recommend using the Pro version of the Tokens Studio, since it provides multiple important features. Let's go through the typical setup of the plugin with Reshaped.
Start with enabling an external storage of your choice to store the tokens data. On the screenshot we use Github for storing the themes since it provides a more granular control over fetching and uploading the tokens data.
For more detailed steps, check the official Tokens Studio documentation:
Now that synchronization is ready, you can start adding the themes to the plugin. Note that we're using the Pro version of the plugin in this example, since it gives us access to swapping native Figma styles and theme management feature.
With both color modes added, you can now go to any other file and start using the plugin there. Make sure that your plugin is still using the same sync provider in those files.
You can switch the theme in the theme management menu and picking a different page. That should automatically switch styles in your file.