Adding an instantaneous electric water heater is definitely an option, but it depends on your home's electrical capacity. Since you're using a 1-phase electricity setup, you’ll need to check if the circuit near the exhaust fan can handle the additional load. Instantaneous water heaters typically require a higher amperage, especially if you're looking for one that provides enough hot water on demand.
It might be worth consulting an electrician to ensure the existing wiring can safely support the new heater. Alternatively, you could consider using a dedicated circuit if you're concerned about overloading. Also, do you need a large flow rate for the bathroom, or are you just looking for something more compact? Would love to hear what type of heater you’re thinking of.