My common bathroom is using this setup too. There's 1 challenge in this design as the heating cut off is triggered differently between storage tank type & instant water heater type.

For storage tank, the heating is cut off by the temperature of the water in the storage. For instant water heater, it is by both the water temperature & the water pressure.

For instant water heater type, I've seen that some are triggered by only water temperature & switch, whereby the switch controls both the on/off for heating as well as the water flow mechanically. If your instant water heater is this type, I'm afraid you won't be able to implement the mixer design.
For the other instant water heater design, the heating only begins when it detect flow & stops when the flow stops or the temperature reaches more than the 'set' temperature.