What you did was edit the alt text on the page and then it was updated on the page. But it is not updated in the media library.
Vice versa, if (what I did) the alt text is edited in the media library, then it won’t show up on the page.
You wrote in your first statement that this is normal and I need to re-insert the image onto the page in order to get the changes that were made in the media library. So if that is a bug in WordPress / Gutenberg and has nothing to do with Blocksy, then we’re good on that count. I can put this forward with the Gutenberg guys.
However, there is another issue: try to use double quotes “like this” for some part of the alt text. This will lead to invalid HTML markup, because the alt-attribute is closed too early. My question was simply whether this is also a Gutenberg bug?