I’m keen on getting to the bottom of this, would you be able to share a full set of steps so I can try to reproduce? I’d like to know if which theme you’re using, whether you’re editing a post or a page, and whether you have the Preview (desktop icon) > Show template option enabled or not.
For what it’s worth, the notes icon should appear if a post or page already has a note, and not otherwise. So if you select a block, click the ellipsis in the toolbar, and choose the option “Add note”, and type in your comment, the note should appear:
Thanks for responding. That’s frustrating, but important to figure out, so I think we need to bring this to the developers. Would you be able to open an issue in the Gutenberg repository about this? The more details, steps to reproduce, information about the site, perhaps even URL, plugins installed, theme, WordPress and plugin versions, the better. If not, let me know and I’ll see if I can open an issue on your behalf.