I always put my "Current Transformer "CT" clamp around the "N" Neutral but it should work exactly the same on the corresponding "L" Live because it detects current passing in and out through whatever heavy wire goes through the hole. I don't know your system but it sounds like that CT from "the isolator switch" (!they add several extra ones with some types of solar and battery) could be monitoring net house switchboard+solar+battery and is the point through which 1.1kW import passed, with the inverter and the battery passing their internal numbers to the smart house controller to minimize import through that CT clamp. Other nearby wires even touching should make little or no noticeable change to the current through the fat wire through the hole.
About units. 3.3 kiloWatts(peak) might describe a moderate sized typical rooftop solar. Last month you write that yours provided 138.9 kWh/month, meaning about 4.6 kWh/day on average, and you'll get more kWh in the summer. kW(p) defining the datasheet performance of the sum of the solar panels under ideal test conditions is great for estimating what to expect, and not to be confused with kWh metered energy.
Your house definitely has at least one large load outside of the solar-battery-import-export zone and it sounds as though that could be the electrically heated shed. Fans use 2 to 40 Watts ( 0 to 1 kWh per day; 1-30 kWh per month) so fans definitely won't account for the extra. Fan heaters on 'I' use 950 to 1100 Watts. With the thermostat, they always use less than 24kWh per day to avoid overheating. 489.5-189.4 = 300 kWh/month = 10 kWh / day billed by the smart meter but not seen by the solar battery controller. In February, that was about half enough heat to keep my whole 2 bedroom house sufficiently warm, but 10 kWh/day is plausible for a moderate sized shed, especially if it has too many patio doors. It sounds too much for a properly insulated shed as that much heat would notice in my 2 bedroom house. Same as for fan heaters, 10kWh/day through an oil filled heater is plausible. You could get that down to about 3kWh/day or possibly less with the heat pump capability of an air conditioner, so here I'll write down enough for you to decide the economics. There are other sorts of machine also called air conditioner. The heat pump type which I mean is similar to
https://www.appliancesdirect.co.uk/p...xCfqtofoUkV8_U
Summer : capability to cool the shed with air conditioner might be desirable and might be a requirement of workplace health and safety.
Late Spring / early autumn : better to just open some doors while it is > 16C outside
Early spring / late autumn : best time to run the heat pump
Winter : you can always buy imported electricity when more heat is necessary than 1-2kW from an air conditioner provides.
Winter coldest day : -6C outside and the heat pump has a sneezy-fit in its cycle which disables it for ten minutes in every hour ? keep the oil filled heater and expect to use both on the coldest day of the year.
Now economics; refine these figures when you know. 10 kWh/day of heating x 182 days per year. Presently provided by oil filled plain old electric heating outside the solar-battery-smart house. Keep the fat power line to the non-solar part of your power supply; is that a second switchboard in the garage near to the smart meter? Consider hiring an electrician to fit an Elster 100C or similar to sub-meter from the garage to your shed. That could be used to show a work expense if there is a company name or a boss. An air conditioner should save about 7kWh/day x 182 days/year = 1274 kWh/year out of 1820 kWh/year present use by the shed. At 25p/kWh, savings are around 318 pounds per year. So to break even in eight years you have a budget of £2.5k
That might be plenty enough to get an air conditioner for the shed, to be used as its main heating (as well as occasional cooling).
Consider changing the wiring to power the shed from inside the smart house solar-battery-controller zone. It might be not worth changing this; you do your sums. I'd have done that from the start, with an Elster 100C showing kWh which your boss pays to you for electricity from your smart house to her shed, at the Ofgem cap price p/kWh, and partly supplied from your rooftop solar electricity.
Now for practical steps to make things better next winter. If you are going to be working from home from that shed long term then it is a workplace and health and safety requirements might define sufficient heating and cooling for the type of work, which might be less active than hacksawing and filing steel parts these days. Since you own the place, it is your job to make it suitable for your requirements.