I don't blame you for being concerned, but I can assure you that no personal data leaves your computer. The processing happens by accessing Gmail metadata and processing on the client-side. Feel free to inspect the source (which is in JS, although it has been minified) or watch outgoing requests.
If the library doesn't exist locally in the browser, the page will load in the same way it loads today (and in browsers that don't support this). Because the feature would only replace known (and working) URLs with a local copy, it's backwards compatible and would continue to work with new versions of the various libraries.
I don't blame you for being concerned, but I can assure you that no personal data leaves your computer. The processing happens by accessing Gmail metadata and processing on the client-side. Feel free to inspect the source (which is in JS, although it has been minified) or watch outgoing requests.