https://sunamp.com/en-gb/hot-water-solutions-thermino-range/
The phase change stuff has positives like taking up less physical space but it's also a much less mature tech than storing hot water.
In the UK there was a unfortunate trend of ripping out these energy storage devices and replacing hot water tanks with on demand electric hot water heating ( only heat the water you need ). And new builds often have no tanks ( as it saves space in the new tiny homes ).
Very short sighted in my view - a very simple way to store energy and everyone uses hot water directly.
One interesting case where "at the same time" actually does happen is overnight car charging. Some chargers are configured to start charging exactly when a cheaper tariff kicks in, which causes big transient issues for the grid. I think modern chargers have a random delay to help with that.
At that scale, it's definitely possible that you all plug in your electric cars and turn on your heat pumps more or less at once on a cold evening after work and start cooking your local transformer. Not my day job but I think it is a potential issue when everything is sized assuming ~2kW average demand or something