I have searched but can't seem to find how I get a client to see newly added Server files with[out] restarting the client.
I assume you have Authentication turned on in the Server settings? "Options > Media Network > Authentication".
Also sync turned on in the Client settings? "Options > Media Network > Client Options (when connected to a Library Server) > Auto sync with server" ticked.
MC should then sync the Server and Client on a "regular" basis. I don't recall the definition of "regular".
The restart MC solution is pretty quick, and can be added as a Theatre View menu option, or a remote control button (with some caveats).
If your configuration is correct, and you don't want to use the restart method, there are two MCC Commands that may work, 20026 and 20032. I haven't tested them, and I don't know exactly what they do. They are under the "File" group of commands, so they may just sync the selected file. You will need to test.
https://wiki.jriver.com/index.php/Media_Center_Core_Commands#FileShare the solution if you get it working.