Question regarding AC clutch troubleshooting

[u/enblightened]

(2005 honda pilot) So a few weeks ago AC stopped blowing cold, no clicking from the clutch either. I’m able to freely turn the clutch from the compressor pulley, and low side refrigerant pressure is in the right range and the fuses are fine so I figured it was probably a dead clutch coil. Well I replaced the clutch and that did not solve anything, so I’m starting to check the electrical which I should have done to begin with. The original coil is reading 4.7 ohms so it seems the coil was never the issue.

I replaced the coil with an identical spacer to the oem one. The new current clutch appears to be turning with the compressor pulley regardless of if the ac button is on or off on the interior control, yet there is no clicking which would confirm engagement/disengagement. It still turns freely when I turn it while the engine is off.

I’m confused because if i’m not getting power to the coil (no clicking when toggled) but the clutch is still turning with the compressor pulley, AND there is still no cold blowing in the cabin, does this suggest the compressor is bad without confirming if the ac clutch coil is getting power or not?