I believe I know what the problem is. First, here's how I think your machine normally operates.

When the power switch (INT1) is on and the other two are off, and the boiler is not up to brewing temperature:
• The Power light (SP1) is on.
• the neutral is connected to the heater and the pump via the safety switch T3 (NC), unless T3 is open due to previous overheating.
• The live wire is connected to the heater via the brew thermostat T1 (NC) and the steam thermostat T2 (NC). The heater is heating.
• The ready light (SP2) is off, as it is shorted by T1 and T2

When the boiler reaches brew temperature:
• T1 opens, removing the short across the ready light and the ready light turns on. (but the ready light goes on and off with the opening and closing of T1).

When the brew switch is (INT2) is closed:
• The live wire is connected to the pump and the brew solenoid.
• The pump already has a direct neutral, so it activates.
• The brew solenoid receives neutral, via INT3 6 & 7 (NC) so it opens.

When the steam switch (INT3) is closed:
• INT3 pins 1 & 2 close, which applies a short across the brew thermostat T1. The temperature rises until T2 opens. The Ready light goes off. When T2 opens, the ready light turns on. (but the ready light goes on and off with the opening and closing of T2).
• INT3 pins 6 & 7 opens, which removes the neutral to the brew solenoid. The solenoid is closed.

NC Normally closed
NO Normally open

Take a close look at the steam switch. You'll see that it's a DPDT switch, each circuit, of which, has an NO position and an NC position. The pins that control the brew solenoid are meant to be the normally closed ones. I believe you have the wires on the normally open pair. You need to move the wire that goes from this brew solenoid to the currently unused lug on the switch.

I actually bought a button in an early stage, because I thought at some point it short circuited, which it did not. My attempt to remove the button also was a great struggle and failure. It seems these buttons are quite horrible. I mean, it would be have been nice to be able to take them out and put them back, but that definitely isn't the case

Thanks about the many replies everybody. I'll go through all posts and take some time to analyse everything. <3

sigissmondo, please update your diagram when you confirm the wiring. I'm in a similar situation as you vis a vis the official wiring diagram vs reality. I have now plugged it in dry, pumped water, and heard the solenoid activate.

By the way, the main power cable has spade lugs (the English name for the female connectors on these devices) on the end, so can be used as a test cable. Plug it into a cheap power bar, and you have a main power testing supply with a switch, and a fuse. You can plug the mains into the pump, or the solenoid directly, although I plugged the AC into the connection on the Anna's switch, and disconnected one side of the pump, and then the solenoid in turn to confirm operations.

Also, I confirm that the solenoid is a NC (Normal Closed) solenoid. That is, you need power for water to flow through

Just so everyone can have a : I started reassembling my Anna, and twisted the screw off a thermostat

I think it may have been damaged previously, but if you're putting in a thermostat, tighten it just a tiny amount past finger tight.

Just to continue with the giggles, I did manage to extract the end of the thermostat screw.