456M HVAC Fan Issues

Does it have the same behaviour with the engine running/not running?

Fan speed control is quite hard to diagnose. Generally, it isn't the control panel as that's just a bunch of resistors, but don't cross it off your list completely. The issue may be a faulty fan speed regulator (aka "hedgehog" or "electrofan regulator" (P/N 64280200)) or the DIAVIA ECU. Over time, the fan tends to wear out and draw more current. This cooks the power transistors in the fan speed regulator. As the regulators are no longer available new (and expensive for second hand ones), the best option is to have the transistors replaced with uprated versions. There are some companies in the UK which do this, but they do warn you before you go through this process to make sure your fan is not about to die completely. How you do this, I don't know, other than listening to the fan for bearing noises. I don't know the typical currents these fans pull.

Repair companies in UK
https://www.technozen-electronics.co.uk/mg-zs-rover-45-climate-control-repairs/
https://berlinettaengineering.com/products/electric-fan-regulator-ferrari-64280200

I haven't heard of companies outside the UK which repair these devices.

Anyway, try a battery reset, maybe try resetting the connectors on the ECU. The ECU performs a calibration test on some of the components after a full power down. Then run your car up to temperature and see if the fan behaviour changes. I'm currently having similar issues with my system (F355). It's just so hard to diagnose without being able to swap out components (with known good ones). The Ferrari professionals have tools to interrogate the ECU for faults, but I'm not sure if this particular fault will trigger any codes.

 

The ECU is on the left hand side of the evaporator unit (inside the cabin)

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The fan speed controller is on the right hand side (550 version shown):

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(also inside the cabin)
Good luck getting to the screws on these.