Heating problem IS a power problem given the high efficiency of heat pumps nowadays. And yes they work perfectly fine in Germany's relatively moderate winters.
There are around 350k heat pumps in Germany right now, of 40 million households (ignoring offices, ignoring multi family homes etc).
There is no way Germany could install enough heatpumps to counteract the Russia induced gas crisis, not even over a timeframe of a decade or more. Optimistically you could fix this by 2050.
So yes, there's a heating crisis, not an electricity crisis.
There are however countries who focused on the infrastructure/consumer side of the equation. When communal or heath pump based heating is significant cheaper, suddenly people interest to invest into home improvements goes up. As the report describe, it not obvious which strategy is best in order to reduce pollution.