If you wish, you can perform some testing with the Klima relay disconnected. If you monitor the single pin from the PBU, you can instantly determine if the PBU is the culprit.

The pin is a ground connection. The PBU provides the ground to engage the relay inside the Klima.

LMK if you want to perform this test prior to taking the PBU apart. I'll look up the details of the pin.