In that message output mode, copying with the mouse indeed isn't possible. Only a few paging commands are available there. So, that "feature" doesn't exist yet.
There are several ways to obtain the output. The most generic is via
:redir, e.g. into the unnamed register:
For a single (last) error message, you can also directly access this via
In the terminal, you could also disable Vim's mouse integration via
:set mouse=, and then use the terminal's mouse drag to copy the (visible) text.