Existing tags appear in the editor when you type at least two characters of it. A list of matching tags appear below the tag input. You may select one of them to ensure spelling it as the existing one, or else you will add a new tag.
No existing tags are just shown without typing in the block editor. In the classic editor there is a “Most popular” tab to see them.
Only tags that are actually used on a published post are shown in the tag cloud widget. Add some and check again.
Thank you Knut, all sorted 🙂