You could plug the bluetti into wall power and while there is wall power it runs off that like a UPS.

That setup I believe would also use solar while it was producing, but the moment solar was gone it’d switch to the house power.

If the overall load is more than house power can give via an outlet (you coupd add a beefier outlet) it’d start draining the battery.

I dont know if bluettis software says use solar / battery only until battery is 10% kinda thing so this might not be optimized to use solar properly.