When first setting up Buy on Google in Sales & Orders for your BigCommerce or Shopify store, step 5 of the setup wizard requests access to Google Merchant Center:

This linking is OPTIONAL as it only indicates to Google Merchant Center support that you are utilizing our app for syncing orders from Buy on Google / Shopping Actions.

After choosing to link, you may note this connection in your Merchant Center account by navigating to Linked accounts > Partners: