I found something interesting.
In C:\Users\username\AppData\Roaming\Steinberg\Cubase LE AI Elements 12_64\UserPreferences.xml
There is nothing concerning the visibility tab in the project left zone setting.
<item>
<string name="Group" value="CustomSettingsProjectPageLeftZone"/>
<member name="Values">
<member name="Setup">
<member name="InspectorID">
<int name="Order" value="0"/>
<member name="Children">
<member name="InspectorInfoView">
<int name="Order" value="0"/>
</member>
<member name="EditorInspectorID">
<int name="Order" value="1"/>
</member>
</member>
</member>
<int name="variant" value="-1"/>
<int name="Variant" value="-1"/>
</member>
</member>
</item>
I tried to tweak around it, but the visibility is still gone. Even after I remove the Cubase and its related settings scattered in multiple places, and reinstall it, there is no hope.