Propper term to search for this setup?

Hello all,

Buying my first sfh and unfortunately there are trees around me and solar companies tell me I will get 60% of max sunlight.

So instead I have been looking at just getting something like enphase, tesla power wall etc batteries. To last a day to two power outage. That's fairly straight forward.

The other thing I been looking at is just getting something like the anker f3800 or something that I could use to just power critical stuff while turning off everything else.

My question is I am having trouble searching for how you would connect the f3800/f3000 or like system to your house power. Is there a term for connecting these smaller systems to the house? Or can you only plug your appliances directly into them and not use house power outlets?

Want to look up the cost difference and what needs to be done by an electrician. But when I search I get how to build diy batteries not how to connect them to house. Or I get enphase install tutorials

Thanks, if I was not clear please let me know!

Ps I see there is something called plug and play solar but does not seem to be legal in usa yet except Utah.