How to partially drive a load with respective impact on my electricity meter?
OK... since you are on the grid, having batteries would be a waste of money, so I suppose you have no batteries.

The answer to your question likely depends on your solar UPS, so check its manual for a feature that would do what you want, and post a comment.

Failing that, the problem is likely to be very complex. If the UPS does not cooperate, then you'd need to measure the power draw for the entire house, combine that with the solar power data, and use some sort of controller to switch your loads.

If you have a very long mains cable between your house and the transformer, then voltage might be an approximation... then again maybe not.

Instead, I'm gonna go on a tangent...

Let's say you got a refrigerator and a freezer. If you put a few bottles of water in there (or more high-tech phase change materials) then you can store cold. A simple timer will then let the freezer/fridge run only during the day, so it runs on solar instead of mains.

Same for your water heater.

I mean, it's a super dumb solution. Timers don't know if the weather is sunny or cloudy... but if the appliances are switched off at night, at least they have a higher chance of running on solar. The total amount of energy used won't change much.

Since you are aiming to save money here, you gotta weigh in system cost and complexity. A pair of $5 timers has very little chance of being a bad investment...

I mean, if you can usefully employ, say, 1kWh per day instead of giving it for free to the electrical provider, you're looking at something like 5 bucks a month. Always good to have, but not something worth spending lots of time, energy and money achieving.