EDIT: In the meanwhile a reload button has been added to the file explorer widget.
Use the workbench.action.reloadWindow command.
Go to File -> Preferences -> Keyboard Shotcuts and define a shortcut for this command. On my system it's placed on Ctrl+F5. The entry in keybindings.json looks like this:
You shouldn't need to reload the entire window, just the folder list. Reloading the window will kill terminals, lose undo history, etc. You can do this using the refresh button in the explorer (second from the right):
If you find you need to do this a lot you can add a keybinding for it, for example:
If you hover over the workspace root in the navigator, four icons appear to the right of it. The third of those icons, a circular arrow, is Refresh -- it reloads the file list.
Right-Click your sln (Will say 0/n solutions)
In the bottom row of dialog it will say reload project solutions.
If it's not present, then it was just reloaded most likely. Try to run build again.
Then you have to find "Refresh / sftp.remoteExplorer.refresh" in the result list.
Click the entry, then click the plus sign before the entry, then press your desired shortcut and hit "enter". I took "Ctrl + Alt + F5" because this has not been used for other commands already.