Rsyslog forward log with space in path or name

I don't know how to do this in legacy mode, but it is easy in RainerScript, which your rsyslog probably supports. Replace all by

module(load="imfile" PollingInterval="10")
input(type="imfile"
    File="/var/lib/plexmediaserver/Library/Application Support/Plex Media Server/Logs/*"
    Tag="plex"
    Severity="info"
    Facility="local3")
local3.* @@10.0.0.5:514

Note that although there is a parameter stateFile="stat-plex", it is deprecated and may not work well for glob files. You are supposed to let rsyslog handle the state file name itself.