I don't know if its Shopify Chat or Apple Chat but the button just won't go away. Even though in the settings of Shopify Chat I can see that the button is not active I can still see the button on the site. Does somebody know how to delete Shopify chat and Apple chat completely?
What theme are you using?
I had the same problem, you can go to Settings > Sales Channels > Apple Chat and click the trash can/delete icon. This will uninstall the App. I'm not sure why it doesn't show up in the Apps tab.