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Could be the bearings as Spyre uses the same BB and ramp mechanism as the BB7 to move the pads. Do you pretension the arm prior to securing the cable (i.e. the arm sits naturally at 5 on the clock dial and you move it to 4 and then tighten the bolt) ?
Hard to explain this unless you've dismantled a BB7 or Sypre but here goes: The above will cause the BB to be already on the ramp prior to the brakes being engaged and when you do brake, the BB will be sitting at the highest point of the ramp hence the noticeable movement.
I've seen plenty who tension the arm to move the pads closer to the rotor which leads to the noticeable movement/sound. The correct setup is to leave it at 5 and then dial in the pads to get it closer to the rotor.
Or your pads might be misaligned and one of the legs of the spring is in contact with the rotor.
Disc brake novice question: front Spyre makes a single tickclick sound when engaging; nada on the back. Ideas?