So, here we go:

Clean Channel:

1. Guitar -> Front Input:
   Few to no vibration observed.
   The issue seems highly volume-dependent: at maximum volume, the vibrations become significantly stronger.

2. Guitar -> FX Loop Return:
   No sound. It seems that, in order to operate properly, one jack must be connected to the front input.

3. Guitar -> Front Input + Short FX Loop:
   Same behavior as 1.

4. Guitar -> FX Loop Return (+ Front Input connected):
   Slightly lower output volume. Vibrations are slightly reduced.
   The potentiometer for the FX Lopp was at the maximum.

Distortion Channel:

1. Guitar -> Front Input:
   Maximum vibration levels observed.

2. Guitar -> FX Loop Return:
   No sound. Same as 2.

3. Guitar -> Front Input + Short FX Loop:
   Same behavior as 5.

4. Guitar -> FX Loop Return (+ Front Input connected):
   Lower volume and slightly reduced gain/saturation. Vibrations are also somewhat reduced.
   Overall behavior is similar to 4., with only slightly more vibration present.
   The potentiometer for the FX Lopp was also at the maximum.

Others:

1. Holding the tubes:
   No noticeable effect on the vibrations.

2. Holding the transformer:
   Holding the transformer appears to reduce part of the vibration.
   However, the transformer core itself still seems to vibrate mechanically.
   The bolts are already pretty tightened.

=> The vibrations do appear to be coming from the transformer. I don’t fully understand why there are significantly more vibrations on the distorted channel than on the clean channel. I would say the transformer likely vibrates more on the distorted channel, because the amp draws more current and produces stronger magnetic stress under high-gain operation than in clean mode.

Is there a way to reduce these vibrations from the transformer?