Publishing Chrome Extension directly from Github

I have my chrome extension (the one's I authored) hosted on Google Chrome store. I did create a developer account (5$ one).

I'd like to link my chrome extension to it's github repository and automatically update it every-time I update the code instead of manually zipping it and uploading the zip file. Is there a way to do that? I couldn't find anything here https://developer.chrome.com/docs/webstore/publish/

There is a self hosting section but I don't think that helps with what I'm trying to. Has anyone figured out an automatic deployment from github to chrome store?

You can consider using a GitHub Action, like for instance Chrome Extension upload & publish

That way, the zip/upload process will be automated.

Example:

uses: Klemensas/chrome-extension-upload-action@$VERSION
with:
  refresh-token: 'xxxxxxxxxxxxxxxxxxxxxx'
  client-id: 'xxxxxxxxxxxxx'
  client-secret: ${{ secrets.CHROME_EXTENSION_SECRET }}
  file-name: './extension.zip'
  app-id: 'xzc12xzc21cx23'
  publish: true

As commented by wOxxOm, make sure to set the client-secret value as a GitHub Secret, as shown here.
In the example above, I reference a secret named 'CHROME_EXTENSION_SECRET' that you must define first in your GitHub repository which has the sources of your extension:

${{ secrets.CHROME_EXTENSION_SECRET }}