Electrons are fungible — you can't tell the difference between one electron and another. Therefore, no actual switching is required — your power meter simply measures the net power consumption of your house, which is the difference between what your loads require and what the solar array is providing.
In some jurisdictions, if that net value becomes negative — in other words, you're generating more power than you need — the meter does measure the power that you're feeding into the grid separately, because the rate at which you sell power to the grid is not the same rate at which you purchase it.
While the panels may be capable of supplying a certain amount of power, this doesn't matter until there is sufficient load to consume that power. So if there is not a sufficient load, the current drawn from the solar panels will drop while the voltage will remain high if there is sufficient sun.
Solar panels need to be presented with an optimum load to maximize the power available from the panel. This is because if too much current is drawn from the panels, the voltage begins to drop. So the inverter tries to find a load that maximizes the power (Volts * Amps) from the panels but only if the inverter requires the power. This is called MPPT - Maximum Power Point Tracking.
In the screenshot that you posted your inverter is consuming 416 watts (26 volts * 16 amps) from your panels. Some of this is going toward the AC load on the inverter (289 watts), some is being used to charge the battery that is at 80% of capacity, and the remainder is inverter/charger inefficiencies. Nothing seems out of order.
In an inverter/charger system, you have two primary sources of inefficiency: the battery charging circuit that must regulate the solar panel voltage to match the desired charge voltage profile and the AC inverter that converts the DC bus to AC. When you are drawing power from the battery, you are effectively multiplying the efficiencies (1-inefficiency) of these two subsystems albiet over a longer time frame generally.
If you would like to test your system more rigorously, pick a day when there is full and directly overhead sun. Make sure the battery is fully charged so that all solar power is available for the AC inverter. Make certain the solar panels are clean. Then start to add AC loads to test how much power your system is able to deliver from solar alone.
Your solar panels can only provide 1000 watts (4 panels * 250 watts) of power to the inverter. And this is under optimal conditions. If you assume 90% inverter and infrastructure efficiency, the maximum power the solar alone could provide is 900 watts. After that the inverter will begin to draw power from the battery. If we assume 5 hours of usable sunlight per day, this means that your system is capable of supplying a maximum of 4500 Watt-hours of energy on an average daily basis. If some of this is drawn from the battery, this number is reduced due to the stacked inefficiencies explained earlier.
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