bug#37840: Missing in the Emacs manuals:

[martin rudalics]

>        (message-bury buf)

'message-bury' calls 'bury-buffer' in a pretty contrived way instead
of simply calling 'quit-restore-window'.  But as long as I don't know
what it is really supposed to do, I can't change it.

In practice, this means that you have to include a 'dedicated' entry
like

      ("[ ]?mail[ ]?" (display-buffer-reuse-window display-buffer-pop-up-frame)
        (reusable-frames nil)
        (dedicated . t)
        (pop-up-frame-parameters
        (tool-bar-lines . 1)
        (left . 859)
        (left-fringe . 2)
        (top . 183)
        (height . 32)
        (width . (text-pixels . 837))
        (font . "SF MONO-18")
        (line-spacing . 3)
        ))

and I will add an according advice to the manual once your setup has
stabilized.

martin