ASHP tank not providing heat to storage plant loop

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@Archmage's answer is somewhat along the right lines in that the heat pump tank wasn't providing any flow, and also that there is a difference in how water heaters operate when the use side is connected to a plant loop. But it wasn't down to a lack of demand. The IDF already had HeatExchanger:FluidToFluid objects set to UncontrolledOn so that part of the demand was already there. That can be seen by the mass flow rate of the Primary HW Loop Supply Side Outlet.

The problem was that I was missing a Use Side Design Flow Rate field on the water heater that forms part of the WaterHeater:HeatPump. From the mixed water heater docs:

Field: Use Side Design Flow Rate

This field is optional and is used to specify the design flow rate through the Use Side of the water heater. The volumetric design flow rate is specified in m3/s. The field is needed when the Use Side is connected to a plant loop. The field can be autosized. If autosized, then the input file should include a Plant Sizing object for the plant loop. Sizing results are reported in the EIO file.

The key part being "The field is needed when the Use Side is connected to a plant loop." This is an optional field, the water heater I was using as a template didn't have one. It wasn't till I went back through the example file HeatPumpWaterHeater.idf that the difference became apparent.