Why Gazebo's/pose/info is changing dramatically when robot is not moving?

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I have the same problem. It can be due to mass/inertia settings of your model's links.

You can also try to add these lines to your world file between the world tag :

<physics type="ode">
  <max_step_size>0.001</max_step_size>
  <real_time_factor>1</real_time_factor>
  <real_time_update_rate>1000</real_time_update_rate>
  <gravity>0 0 -9.81</gravity>
  <magnetic_field>0.000006 0.000023 -0.000042</magnetic_field>
  <ode>
    <solver>
      <type>quick</type>
      <iters>200</iters>
      <sor>1.3</sor>
      <use_dynamic_moi_rescaling>0</use_dynamic_moi_rescaling>
    </solver>
    <constraints>
      <cfm>0</cfm>
      <erp>0.2</erp>
      <contact_max_correcting_vel>100.0</contact_max_correcting_vel>
      <contact_surface_layer>0.001</contact_surface_layer>
    </constraints>
  </ode>
</physics>

This reduce the robot movement for me.