You didn't mention which position it is in but it changes which arrow keys are used.
It doesn't matter which position the message window is because I wrote those words:
[...] then tab-browsing with an arrow-key is not possible. [...], I can not put the content-area of the tab in focus by pressing 1x an arrow-key.
On the machine that I use, I can't tab-browse with any of the arrow-keys in the message window, no matter if the message window is on top or at the bottom, no matter if the tabs are ordered vertically or horizontally. And on the message window I can't put the focus on the content-area of a tab with any of the arrow-keys, no matter if the message window is on top or at the bottom, no matter if the tabs are ordered vertically or horizontally.