The power word here is SIMULTANEOUSLY . Many inverters can have "priorities" set but what they do is SWITCH between solar and grid. One or the other, NOT both in the same time.
Any grid-tied inverter "mixes" grid power and inverter power. Since grid, inverter and load are connected to each other (as long as grid power is available), the mixing happens by itself due to Kirchhoff's current law. Consequently the following relation holds:
Consumed utility power + generated inverter power - load power = 0
or
Consumed utility power = load power - generated inverter power
A grid-tied inverter can decide (based on other criteria)
how much power it generates. If it generates less power than required by the load, then the missing power is drawn from the grid. And if it generates more power than required by the load, then the surplus is exported to the grid (because the current pushed out by the inverter has to go somewhere if it is not consumed by the load).
To better understand the cross-relationships, it helps to understand that a grid-tied inverter rather act as AC
current source, while the grid acts as
voltage source, and an off-grid inverter acts as
voltage source, too. I.e. a grid-tied inverter is regulated to push out a particular amount of AC
current, while an off-grid inverter is regulated to provide a stable 230V AC voltage (and the current is then determined by the load).
Easun's all-in-one inverters have either "ISolar..." or "IGrid..." model names. The "ISolar" models are off-grid inveters and can only
switch the load between utility and inverter. The "IGrid" models, OTOH, can also be configured to run the inverter in grid-tied mode. I pointed you to an "IGrid" model. The manual is unclear how load powering priorities and "hybrid output function" (grid-tie mode) interact, but I guess that the priorities are still honored in hybrid mode. It would not make sense not to honor them.