The API shows this and this. Looks like in both cases, not just no comment, but not even user ID. Tried to navigate there using the coords mentioned in the API, but of course they don’t show up on map. And the close_url mentioned in the API doesn’t work (I guess it needs to be called by a function and authenticated and not just by visiting it in browser).
You were I think on the correct way by trying using the API but like you already noted, to make changes you need to be authenticated.
I would try to download the notes in Josm and if that works use Josm to close them. I could not test it as I do not know the coordinates, I do not see the coordinates in the API links you shared.
But just when wanted to close the note I noticed the not seems to be deleted, the code that was working earlier gives ElementNotFoundApiError(404, 'Not Found', b''). Same for the other note.
Of course there’s no user id if a note has no visible comments. The id can only be on a comment.
And it’s not the only bug related to such notes. The note layer on the osm website is also broken. Not only it won’t show you notes without comments, it will also drop all earlier notes in the same view.
There’s a zero-comment note on the airfield which you won’t be able to see on osm.org. But can you see this note while the airfield is visible by opening the first link?