All the statements are consistent except for your "does not regenerate while coasting". "Engine braking" is done by spinning up the ICE both in the TCH and in conventional cars. This absorbs energy, but does not regenerate. "Coasting to a stop" would be the condition where the foot is off the accelerator and speed is being lost. This regenerates in the TCH to mimic the effect of engine braking in an automatic transmission-equipped car in "D", however there is no engine braking -- indeed the ICE isn't necessarily spinning.

The only real engine braking occurs when in "B", engine braking is simulated when coasting, and friction braking is simulated under "light braking". Only the latter two regenerate.