When selecting a gameObject with a camera as child and using local orientation, camera is considered pivot point, no matter which child is selected. Unity 2021.3.7f1.
Upper left is buttons: pivot / center and global / local… start toggling.
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I am afraid your comment is no help or use. Quite obviously these options are to be used for editing. Like I stated, having a camera as child messes that up. Therefore you cannot edit as per normal.
Could you update to the latest LTS and record it if still there?