Is It Possible to Use the Block Editor’s Notification Feature to Send Another Notification After the Post Is Saved?

Yes, but you have to do it Redux- way. Subscribe to post saving action (there are separate actions for save and auto-save) and dispatch a message using dispatch function.

Edit:

Inside blocks, there are better hooks to use, like useSelect. But, outside the block, in general block editor environmentm you have to use subscribe. In subsbscribe you are subscribed to every action dispatched to block editor. Inside the listener function you use wp.data.select to test current state of the store. You want to test isSavingPost and isAutosavingPost selectors.
https://developer.wordpress.org/block-editor/reference-guides
https://developer.wordpress.org/block-editor/reference-guides/data/data-core-editor/#issavingpost/data/data-core-editor/#isautosavingpost

To wrap everything up:

const unsuscribe = wp.data.subscribe(() =>
        {
            if (wp.data.select('core/editor').isSavingPost() || wp.data.select('core/editor').isAutosavingPost()) {
   // your code
}

        });