With the attached file, start emacs as:

  emacs -Q --load bug.el

and then move the point left or right.  Originally I started to write
this file as demonstration to bug#42421, but you fixed the bug faster
than I could find time to finish it.  Now, I think everything works as
documented, but with the help of this recipe, I'd like to argue that
eldoc-prefer-doc-buffer is a bit annoying in this case.  Its
documentation says:

   Prefer ElDoc’s documentation buffer if it is showing in some frame.
   If this variable’s value is t and a piece of documentation needs to
   be truncated to fit in the echo area, do so if ElDoc’s documentation
   buffer is not already showing, since the buffer always holds the full
   documentation.

I think it would be better to show the documentation only in the *eldoc*
buffer and not in the echo area even if the documentation doesn't need
to be truncated but the echo are needs to be resized to display the full
documentation.

(bug.el changes eldoc-documentation-function to circumvent bug#42531,
which I reported few minutes ago, but changing the order of the hooks in
eldoc--eval-expression-setup, doesn't seem to fix bug#42531)

Thank you, João, for your work on eldoc.