Cascading Common-Emitter Common-Collector for maximum power transfer
Let's say the base of Q2 is biased to an average voltage of Vbias. Ideally, C3 would be charged to an average voltage of Vbias minus Vbe_of_Q2.

When the signal going to the base of Q2 is in the positive phase, it would be higher than Vbias, Q2 turns on. The output impedance is similar to your calculation, being the combination of the output impedance of Q2 and RE2.

But when the signal goes into the negative phase, it would be lower than Vbias. Given the voltage charged across C3, current flows backward, and Q2 turns off. Now the output impedance is simply RE2. RE2 cannot drive Rload because it is 100 times of Rload. Therefore the lower part of the sine wave signal is lost at Rload.

It is actually worse than the description above because C3 would be charged to an average voltage higher than Vbias minus Vbe because of the imbalance. So I actually cannot explain why the yellow trace only lost about half of the sine wave and not more.