Do you still have the original session? Can you reproduce the problem?
If you hold down
Shift keys while clicking the Open in PuTTY, WinSCP copies the command to execute PuTTY to clipboard (instead of actually executing PuTTY). What the command is?
The problem is reproducible. When I use Ctrl Shift the result for either pull down "Open in PuTTY" or icon "Open session in PuTTY" is
"C:\Program Files (x86)\PuTTY\putty.exe" -load LinuxTB
where LinuxTB is the name I had given to that site.
The effect is a new window in which top bar shows an intended destination, e.g.
(where aaa-bbb-ccc are actual numbers).
The problem is that the actual Public DNS (IPv4) for the correct destination is not
(where xxx-yy-zzz are completely different actual numbers).
So I'm not surprised at all that it fails. I am surprised that it isn't trying to go to the same Public DNS (IPv4) that I have specified clearly as my "Host name:" for the site.
I have an unconfirmed suspicion that the destination that it is trying to use might be the former "Host name:", which needed to be replaced due to a change of the virtual host. Otherwise, I have no idea where it is getting the wrong destination host name.
If I Clone everything as a New Site with default name of "LinuxTB (1)", the new cloned copy works correctly, even though I did not change anything apart from just making a clone.
Interestingly, for the cloned version, the result for the Ctrl Shift test is this.
"C:\Program Files (x86)\PuTTY\putty.exe" -load "WinSCP temporary session"
If I try a different site altogether, it also gives me this second result, not the site name.
For one last bit of weirdness, when no one responded for a few days, I deleted the original bad "LinuxTB" Site entry and renamed the working "LinuxTB (1)" to "LinuxTB" (the original name). So I was afraid that the behavior would no longer be reproducible when I saw your reply. However, the "new" version of "LinuxTB" also fails just as before, while making a new Clone also succeeds just as before.
Other than the PuTTY problems, I have not noticed any other operations that have problems or confusions about the destination site. The normal WinSCP connection works. The "Open terminal" Console works, both as a pull down and as an icon.