Currently, the conversion to methane gas using the Power2Gas method achieves an efficiency of 70%. It is certainly not a cure-all, but a possible component. The heat pump with battery you mentioned is also still far from being a solution. When I look at the surcharges for heat pumps, I need a certain consumption for it to pay off. Batteries are just now reaching breakeven in terms of amortization capability. There is still a long way to go.
And another problem is that solar power is mainly available in summer, while heat pumps mainly consume in winter.
As I said, Power2Gas can also be a puzzle piece.