I think you are thinking of something very different than what "heat pumps" actually are? They don't involve storing heat, they're just an inverse fridge.
"A heat pump is a device that transfers heat energy from a source of heat to what is called a thermal reservoir."
So yes, it involves energy storage.
The way this works is you store heat in the summer (warm up a lot of rock or ground underneath your house) and recover that energy in the winter by pumping a liquid through warm rock back to your house and use it as a heat source.
The air outside your house counts as a thermal reservoir as well. That it doesn't store anything to the next season is annoying and makes it not work well in cold temperatures.
I think wikipedia is wrong or confusing here. A heat pump requires a thermal resevoir (something that doesn't change temperature much when you move heat to or from it) of some sort, usually the atmosphere, or in ground source heat pumps pipes running through the ground, but it can move heat in either direction.
> While air conditioners and freezers are familiar examples of heat pumps, the term "heat pump" is more general and applies to many heating, ventilating, and air conditioning (HVAC) devices used for space heating or space cooling.
Basically what I would understand from the term heat pump in ordinary conversation would be an air conditioner intended for use in a heating dominated climate rather than a cooling dominated one, but there might be some regional differences in usage.
Thermal reservoir is a technical term in thermodynamics and as others have pointed out it doesn’t mean what you think it means. Anything remotely resembling a (reversed) Carnot cycle would involve thermal reservoirs. You can read its own Wikipedia page.
https://en.wikipedia.org/wiki/Heat_pump
The first sentence:
"A heat pump is a device that transfers heat energy from a source of heat to what is called a thermal reservoir."
So yes, it involves energy storage.
The way this works is you store heat in the summer (warm up a lot of rock or ground underneath your house) and recover that energy in the winter by pumping a liquid through warm rock back to your house and use it as a heat source.