Simple Gallery Pro (https://f-droid.org/packages/com.simplemobiletools.gallery.pro) should do it. Just a quick tip — I’d advise to use the last version from the v6.23.x line and not the newest one. They updated the target SDK in the meantime and with that lost the ability to list only selected folders and hide everything else. In the older versions, you could ignore all first (i.e. add the whole internal storage to the excluded list) and then add only specific folders to the included list.
When it comes to the parent/child folder view itself, you should be able to get it by using the following settings.
Aaagh… level 1 and level 2 on the same screen, no images “download” and “gettyimages-…”.
Simple Gallery Pro has no nested folder support now.
You could also just use a file manager to navigate the nested directories. For example:
It has an integrated gallery and image viewer. Note you shouldn’t access the “Images” category from its main screen, but just navigate the folders in the main or external storage. The category view will coerce everything to one level as well.
Eh, while obviously the way they display folders isn’t the same as Windows Explorer, it does still provide a method to browser subfolders in a way that other gallery apps normally do not. Also, it’s a free and open source app (see https://github.com/SimpleMobileTools/Simple-Gallery), so you may also try to post your feature request there and maybe someone will see it any implement the changes (which of course may take time and/or may not be guaranteed at all, but that’s usually the way the open source world works, unless you hire someone to do the changes for you).
In this specific case, as @acolomb has already mentioned, you may be better off simply using a file explorer. If you want something that’s free and open source, Material Files (https://f-droid.org/packages/me.zhanghai.android.files) does come with a built-in image viewer as well.
I can definitely say that improvements should not be expected.