To be clear (so there must be no problem here):
1.1. You Set Local toggle in Scene View (it’s relevant for Scene View only).
1.2. Rotate around Axis uses Local axis by default based on this.
1.3. The Inspector shows Local values in Transform.
Vector3.up — is a global axis. GameObject local axis can be got from transform.up. Example.
Next, you didn’t provide inspector screenshots of these 3 objects. There can be a rotation in the hierarchy that changes the coordinate system, and you experience the expected result.
For example, as you can see in all 4 objects related to camera in my Football, there are no rotation changes and no such issues: