I apologize, Martin: you responded promptly and offered a test version of WinSCP for me to try, and I still have not tested it. It's just been a very busy month. :(

I have added this issue to the tracker:
Issue 2037 – Allow normal behavior of double-click on a file even when resolving of symlinks is disabled

I'm sending you an email with a development version of WinSCP to the address you have used to register on this forum.

Yes, that's the problem.

Oh, wait: I think I see the problem.

When the user double-clicks a directory, WinSCP navigates to that directory.

When the user double-clicks a file, WinSCP copies that file (or opens it, or edits it, depending on the double-click setting).

But if "resolve symbolic links" is turned OFF, WinSCP does not know whether the target is a directory or a file? Is that it?

I had not seen that documentation.

If not a bug, I guess this is a feature request:

• If "Operation to perform on double-click" is "Open", then WinSCP should attempt to open.
  
• If "Operation to perform on double-click" is "Copy", then WinSCP should attempt to copy.
  
• If "Operation to perform on double-click" is "Edit", then WinSCP should attempt to edit.
  

Well, it's not a bug, it's as documented:
https://winscp.net/eng/docs/ui_pref_panels#double-click
Though the question is how to resolve your use case now.
I'll think about it.

If I change the settings to

• Session >> Sites >> Site Manager ... >> (select a site in the left pane)
  >> Edit >> Advanced ... >> Environment/Directories >> Resolve symbolic links is NOT CHECKED
  
• Session >> Sites >> Site Manager ... >> (select a site in the left pane)
  >> Edit >> Advanced ... >> Environment/Directories >> Follow symbolic links to directories is NOT CHECKED
  

Double clicking an image in the remote pane still attempts to open the file like a directory, and fails, because the file is not a directory: it is a *.jpg image.

Version 5.19.4

• Options >> Preferences >> Panels >> Double-click is set to "Copy"
  
• Session >> Sites >> Site Manager ... >> (select a site in the left pane)
  >> Edit >> Advanced ... >> Environment/Directories >> Resolve symbolic links is NOT CHECKED
  
• Session >> Sites >> Site Manager ... >> (select a site in the left pane)
  >> Edit >> Advanced ... >> Environment/Directories >> Follow symbolic links to directories is CHECKED
  

Double clicking an image in the remote pane attempts to open the file like a directory, and fails, because the file is not a directory: it is a *.jpg image.

If I change the "Resolve symbolic links" to CHECKED, then double-clicking the file transfers it. NOTE: the file is not a symbolic link: it is a *.jpg image.

I believe this is a bug.