I have in very large houses and hotels seen a system where a pump circulates the hot water so no delay at the taps, is that what you have? Standard central heating with S Plan
View attachment 333273 the same timer which works the central heating also selects DHW no reason they can't be two independent timers, but tradition has them in one programmer (fancy name for timer) but there are some rather complex systems, but these are normally associated with solid fuel, it takes time to allow a solid fuel fire to burn out, so the systems need to allow a reserve where the heat can be dumped. And also likely a back up, should one not want to light the fire so we get systems like this
View attachment 333274 I have only come across this system once, in my brother-in-laws old house, the tanks are that heavy the floor needs to be rather strong, for safety in case of power cuts the tank needs to be where thermo syphon can work, I never looked at the electrical side, it is not a system that can cost effectively be retro fitted, so has to be installed as the building of the house.
This is the bit which is making me think you have some thing out of the ordinary. My house is also out of the ordinary with CH and DHW due to having a garage made into a granny flat, so this is only heated when we have visitors, so central heating both uses motorised valves, pumps, and programmable TRV heads. Normal is one or the other, not both as they in essence do the same thing.
I thought to start with only talking about DHW, but having it independently controlled for three floors does not seem normal. I know some CH systems do that, but unless like me with what is really a separate dwelling but using same CH boiler, it seems wrong to split into floors, as at the moment I am still using top floor, which has two bedrooms, an office and craft room. Down stairs we have living room, dinning room, and kitchen. So both floors used during the day, therefore using programmable TRV heads is far better as we can select room by room what is heated.
I can select DHW to be heater in summer by oil but with solar panels I use electric, but if I did not have solar panels I had to use time as no tank thermostat, but if I had one, the DHW would not be turned off except for holidays. 40 gallons takes a long time to cool so no point, only other reason for timer is to use off peak power.
Anyway enough of my house, what we need to know about is yours. I fail to understand with a modern well insulated tank why you want a timer? Something missing in telling us what you want it seems.