What does this pipe do?

[Doctor Gollum]

Well, it has to be one of those three things.

But it's not :-(

We fitted a replacement loom today

Tried swapping b1 and b2 sensors and the fault doesn't move

Then we fitted the a different ECU

Despite this - the second the car is started - it logs "open circuit" fault code for the lambda heater on B2 S1

I hate to say it but I'm short of ideas ....

Back to the beginning, I stated that ALL four sensors have a common wire.

If replacing the second sensor fixes it, the the issue might have been on the loom of that sensor. Don't forget that the tail to the sensor forms part of the overall loom.