Why does it look like SpektrRG makes a u-turn in the ground track image?
An L2 injection trajectory looks a lot like going straight away from Earth -- i.e. the ground-track position in inertial space is changing only slowly. Meanwhile, the Earth is rotating Eastward underneath that point, so the ground track appears to move Westward across the surface of the Earth.
How does it manage to orbit the Earth at a steady 6 degrees above the equator?
It's not orbiting around the Earth; it's going almost straight away from a point 6 degrees above the Equator.
Compare the "DM-03 Burn 2" and "Spacecraft Separation" checkpoints on the ground track against the same checkpoints in your lower right image.
It's going from a 170km x 1927km orbit, which is not very eccentric at all¹, to a 500km x million-km orbit, which is practically a straight line by comparison.
Equidistant-time marks on the ground track would help with the visualization (or synchronized animation of both the ground track and perspective views) -- at spacecraft separation the ground track would be going ~10 km/sec across Earth's surface, but the Westward track after the U-turn is Earth rotation speed, ~400 m/sec.
¹ Remember to add Earth radius to the given orbit altitudes.