Looks like the the boiler is overfilling as you said - as if the probe is not able to detect the water level in the boiler.
I’m assuming the water is coming out through the anti-vac valve - showing that the boiler is overfilled.
Did you check the connections of the probe when you removed it for cleaning? Is there continuity? If I remember correctly, Dave used to say they are very prone to breakage when removed or over-tighten.
Did you contact Bella Barista? Espresso Underground used to stock a lot of Lelit spares - not sure if they do anymore.
E.g.: https://espressounderground.co.uk/product/lelit-stainless-steel-depth-probe-pn-mc9600050/
Not sure if that’s the right part nor whether that’s in stock.