What exists right now for someone who wants to make a very small solar project?
this earlier post might give you an idea where to start
In my imagined setup, there would be 1-2 panels on the roof connected to a cheap consumer battery (something like a small ecoflow).
When the grid is present it's much cheaper and easier to feed inverted solar power to the house and draw the A/C power from the house. Since the solar would be small there would never be any power from it reaching outside the house. This meets the "at least offset a lot of its energy use" goal with minimal expense and complication.