Hello,
is the dropdown option "Display images by:" in the image edit page only for a session or a setting? I search a global setting to "manual".

It actually should stick per user and for the backend only. For the backend there is no global option, only for the front end (unless overwritten by individual settings in albums themselves).

Correction: I search a global setting to "manual" for the user admin area.

There is no such global option.

Apparently, the selection in the "Display images by:" dropdown is a global setting. For me is it good.

the behaviour that I can regulary see is as following:
in admin>images, you can see a default order for pictures in albums (I choose date).
for each album, you can overwrite this image ordering, by setting a value in sort sort images by (starting with the default value *gallery image sort order)
if you go on image order tab, you can change the order of your pictures, and sort images by value for this album will be set to manual.

whatever order you choose, it is avaliable on front end and back end.

For this question I was only concerned with the order of the images in the backend editing. (not order the subalbums themselves).
I would like that the order of the images in the editing is exactly as they were sorted by me, so as shown in the frontend. And always with all images in all albums.
Apparently this works if you select on once image editing page from the dropdown "manual". Then even "manual" in the image editing pages is preselected, in which no "manual" or "[numbers]" for the album and parent album and images is entered in the database (albums/images->sort_order).
So as it is, it's good for me. Always "manual". Always as I sorted.

I have missed such a setting only in the options, or not found.
Example: "Display images in editing by: allways as I sorted"

There are two dropdowns in the album editing page.
Sort subalbums by:
Sort images by:
I did not choose anything there.

I don't understand.
'manual' sort order needs a manual ordering of images in image order tab (by drag and drop images), so this specific order is specific for each album and can't be set by default on each album (and this order can't be set in front-end).
you can also change albums and sub-albums ordering by drag and drop them in
the albums and pictures orders are the same in frontend and backend (and are shown in the same way in FE and BE).

According to me, you don't need to select 'manual' for albums or pictures order. this value is automatically setted if you manually change order of your albums (in admin/albums for albums/sub-albums) and for pictures (in admin/albums/image order for pictures of a specific album).

there are default values of gallery order (first level of albums) and images order (in admin/options/gallery for the 1st one, and admin/options/image for the 2nd one). all sort orders of albums, sub-albums and images are inherited by default with these two values

then you can manually change these order values as described above. you can also change order by changing values of Sort subalbums by and Sort images byof each albums or sub-albums.