Plex Library Scans Initiate Hundreds of TCP_WAIT Sessions using up all available ports?

The default. You can add more ephemeral ports.

With an elevated command prompt:

PS C:\WINDOWS\system32> netsh int ipv4 set dynamicport tcp start=32768 number=32768
Ok.

PS C:\WINDOWS\system32> netsh int ipv4 show dynamicport tcp

Protocol tcp Dynamic Port Range

Start Port : 32768
Number of Ports : 32768

That doubles the amount of available ports. See if that works for you.

Philippe