That menu/shortcut pops up a dialog box asking for an "Edit" filename. You paste in an existing file and sure enough, it's like I double-clicked on it.

Thank you so much Martin.

You can use Shift+F4 (Files > New > File) and paste a path to an existing file.

My desire is to have a textbox/prompt appear using something like "!?prompt?!" which I have working already. Then, using the current session, emulate the "edit" function for that file.
My issue is that our test environment has tens of thousands of log files in the log directory, which takes a long time to load in WinSCP. To get the right log takes a long time to load and find. If I could just type/paste the name into a prompt and have it transfer/edit as-if I double-clicked on it in the explorer panel, it would save me some time.

Is this a scriptable thing? "Use the current session to edit a file that I enter" to where I don't need to have a password store in cleartext?

We use SSH, so that's why I want to use the currently logged in session.