Placing only 1 detector in front of one of the double slits ALSO collapses the wave function of both slits. This unequivocally proves that it isn’t the measurement method, but the ACT of measurement itself.
For example, we get the wave pattern. We place a detector in front of both holes we then get 2 bands. ..now, if it were the detector interfering as you mentioned, we will take 1 detector away and leave the other. This way only 1 slit has a detector that interacts with the electron as it passes through.
This would mean the slit with the detector produces a band while the slit without the detector produces a partial striped pattern of the wave.
This is not what we observe however. Measuring just 1 slit still causes 2 bands.
This is because even measuring just 1 slit gives us information on the other. It’s the information that is seemingly the cause of the collapse of the wave function.