How do I wire this motor's terminal plate, and is this motor continuous duty?
I can’t say for certain but I’d be highly confident that this is continuously rated.  Firstly, synchronous motors aren’t well suited to stop-start operations, and if it weren’t continuously rated then I would expect the rated on/off times to be published prominently alongside the power/torque.
I can’t say how to wire it, but I’d expect that there are two windings, one direct across live-neutral and one with that red capacitor in series to provide a phase shift.