I have solar panels (6 kW) and inverter (5 kW) plus battery (6.4 kWh) professionally fitted, but it took me 20 months to get a smart meter fitted and the second MPAN number needed to be paid for export.
In real terms it is the inverter and battery which have gained most, the charging it overnight, on cheap rate, and using it during the day, the solar panels meant battery does not need to be as big, but cost v return, it is the battery which saves the most.
So numbers first, many items in the home use 3 kW, so the inverter needs to be bigger than 3 kW, so it can cover one 3 kW item plus back-ground use, so my 5 kW does seem about right. Yes there will be times when the solar is producing over 5 kW, but that does not happen very often, so the 5 kW inverter with 6 kW of panels does seem about right.
The battery size is more about what it can charge at, and discharge at, batteries charge at around 2/3 of their rating in kWh, so at first used a 3.2 kWh battery, which would only charge at 2 kW, so I was seeing power being exported even when room in the battery, so doubled to 6.4 kWh so now can charge at 4 kW, the inverter can produce 5 kW, but it is rare that other items in the house are not using the extra kW, so a larger battery would not gain that much more solar stored.
Discharging again was only 3 kW, now up to the inverter maximum of 5 kW, so other than the shower, most items are powered by the inverter and battery.
So the unit shown,
seems 2000 watt output, but only to the four sockets on the unit its self can deliver high output, we are limited to 800 watt into the grid, and clearly limited to 3 kW as that's the plug limit, I can't see any CT in the video to limit export, he does talk about monitoring but not clear if this is to give him info or to limit export.
What I can't work out, is how it stops some one buying 6 and running them all at the same time? It is as he says not a fixed installation.