See also WinSCP suddenly opens with two local panels with seemingly no option to open a connection to my server. What do I do?.

You have probably turned off "Show Login dialog on startup..." option:
https://winscp.net/eng/docs/ui_pref_window

Even with it turned off, there are lot of options to open a new session. For example using New Tab > Remote Tab command (on the toolbar or in the menu):
https://winscp.net/eng/docs/task_connections#opening_additional_connection

I get the window which shows the files on my computer, with no means of exiting except to close down.

So what do you get instead? Does nothing open? Or do you get the main window (with file panels)?

When I click on to WinSCP it doesn't give the Login page, so I can't login. I have the latest version of the software. My computer has Windows 11.