How do I fire a snackbar notice in admin?

WordPress has some global actions you can use here. If you want to add your own notice in the lower corner (like the screenshot), you can do that like this:

 wp.data.dispatch("core/notices").createNotice(
        "success", // Can be one of: success, info, warning, error.
        "This is my custom message.", // Text string to display.
        {
          type: "snackbar",
          isDismissible: true, // Whether the user can dismiss the notice.
          // Any actions the user can perform.
          actions: [
            {
              url: '#',
              label: 'View post',
            },
          ],
        }
      );

The important part here is type: "snackbar". You can also leave out the snackbar part and it will appear in the UI above the content:

Here’s the full article on WordPress’ Block Editor Handbook: https://developer.wordpress.org/block-editor/tutorials/notices/