When using the web interface I don’t see any opportunity for entering the alt text.

Apparently, some instances offer it: you might want to ask your instance administrator to upgrade. If yours doesn’t offer it, the text alternative can be adjacent as stated in the success criterion for non-text content

All non-text content that is presented to the user has a text alternative that serves the equivalent purpose

and the techniques for it identified with prefix G. The alt attribute is merely 1 way to accomplish that.

When it’s a screenshot of a webpage, a link to the source makes sense as a text alternative, but it might make more sense to eliminate the need for a text alternative altogether. I see way too many images that could be blockquotes & links, which are often superior to an image: more accessible & more useful to everyone else. That’s often the case of good accessibility: it benefits everyone else.