TLTR, but here goes:
It seems to me that DHW tanks are the trickiest item in a HP circuit to analyse/optimise – fluid properties and temperature differences are changing rapidly with time (so you can’t apply steady state heat balance equations), and it also takes a significant time for the convection pattern to develop (an essential component of heat transfer). Also DHW tanks are prone to temperature layering, which takes time to break up.
Many heat pump controllers do not constrain LWT during DHW heating (unlike space heating where temperature compensation limits LWT), which is a particular problem if the DHW tank coil is undersized – the circulating fluid can get very hot (at a rubbish CoP) before significant heat is transferred to the tank contents, because convection takes a while to get going.
If your DHW demand is modest, or at predictable times, you may be able to programme DHW just once a day (or even two). In this case, one partial answer to energy minimisation may be to heat DHW in two or more short bursts, with a few minutes’ gap between. This (I surmise) allows the convection current to start developing before the LWT has wound itself up too far, and distribute some heat around the tank before the next burst.
In my case I can heat my 150 litre DHW tank from 20degC to 40degC in 2 x 15 minute bursts, with 5 minutes between bursts. Although the total heat required is the same as a 1 x 30 minute burst (obviously), it is delivered at a maximum LWT of 55degC rather than the 60+degC that occurs during a single longer burst, with the consequent improved CoP.
The above observations are for a Samsung HP but I thought it might also be relevant to some Daikin users. Why not give it a try and see if it helps?