Perhaps also useful would be plug in batteries, especially if one has variable rates. Charge when cheap, discharge when expensive.

One constraint on these I've read is that if you have sources and sinks on the same circuit, you might overload the line without tripping the breaker at the box. If I'm understanding this correctly this has caused them to limit the power of plug-in solar to a fraction of what a single circuit could potentially carry.

Problem with this idea is batteries on grid scale are always cheaper per MWh, so grid scale battery operators will eat away any arbitrage you could earn with more expensive consumer gear.

I'm not trying to make money here though. I'm trying to recoup some of my costs for a home backup for when the grid fails. My house automatically switches to a backup generator when the power goes out, but it is from the 1970s and wearing out, a battery system that can recoup some of the costs by arbitrage is useful even if it loses money.

While the power doesn't go out often, it is a big deal when it happens and so a backup is useful. I'm still fixing the damage from the last one - the sump pumps not running for an hour in a rain storm is expensive. Fortunately it wasn't a long outage, much longer and the fridge/freezer would be a problem. In cold weather the furnace is important to keep running. There are other essential things as well that my house cannot survive without. Beyond that I want my computers to keep running if possible.

There's not sufficient grid scale capacity yet, there are lots of consumers arbitraging in the UK.

My electricity supplier sends me a message nearly every week saying if I use less electricity during peak demand times then I get free power at weekends. https://octopus.energy/saving-sessions/

I've been doing this as well! It's always 6pm-7pm for me which is when my Cosy tariff has the peak rate anyway, which I try to not use. So for no behaviour change I normally get 1-2hrs of free electricity on a Sunday morning! I got 15kWh for free this week by having the immersion, heat pump, washing machine and tumble dryer running. Not bad for 0 effort on my part.

It’s way easier to plug in a unit at home than it is to get planning permission for mega batteries.

Yes, it's designed so that total current and potential heat problems are still within safety margins of circuits built according to code. In most of Europe, one regular (or upper end of regular, depending on country) residential circuit can supply 3.6 kW (230 V * 16 A = 3680 W), so 800 W are "just" a 20% overload.

Correct, though it becomes a bit more of a problem if someone decides to connect a few of these (or batteries) to the same circuit