Welcome to HB.
... whenever I start brewing now,a stream of water just pours out of the steam wand ...
Here's a photo of a boiler replacement for a Ariete Cafe Roma Deluxe from a spare parts site:Photo courtesy Creticambi.it
If it is not the exact one, I'm quite sure it is much the same as yours.
It's a step forward from what was my first 'espresso' coffee machine in the sense that it has a three way valve (black thing on the left) and more than one thermal protection.
The brewing temperature seems controlled by a fixed value thermostat on the side while the steam (and over-temperature protection) would be controlled by another fixed value thermostat on top (small brown things).
These units have no other sensors and to produce steam, you throw a switch that overrides the water temperature sensor (probably 95°C) and then the water inside the boiler gets heated to above 100°C, ie: whatever the limit of the sensor at the top of the boiler (usually not above 120°C).
Whenever you are brewing a shot or heating up to make steam, the pressure inside the boiler rises
: when brewing a shot because the pump is working against the puck/pressurised basket and when making steam because of the brew sensor override by the steam switch, heating the water past 100°C.
Now, in this particular design, the steam valve is mounted on the side (in others it is mounted on top) so if the stream valve (brass thing on the right) does not close properly or leaks, water will come out when brewing.
As the boiler is at brewing (and not steam) temperature you see water and not steam come out of the steam wand.
You have to get the unit serviced (probably not worthwhile in $ terms) or you can take apart the valve and see why it is not closing properly.
Not a hard thing to do if you are DIY oriented.
In any case, please take into account that electricity and water do not mix
well and that anything
you do with your machine should be done with it unplugged