How much does a photovoltaic storage deliver?

I specifically chose my inverter so that it can power the entire house at times. When I have the sauna and the basic house noise running, only minimal power is drawn from the grid. In practice, it doesn't matter much, since hardly any storage system will be large enough to supply the sauna evenings that especially occur in bad weather. So even if the inverter only handles 6kW, the storage will be depleted just the same and power will be drawn from the grid just the same – only slightly differently distributed over time.

And be careful: 4kW oven sounds like single-phase. So you should check what the inverter can deliver per phase. These small ovens in the energy-hungry outdoor sauna therefore usually run on continuous fire, meaning the storage will sooner or later be drained.