CE Amplifier voltage gain is not as calculated
For the circuit as drawn, the emitter capacitor has an impedance (magnitude) of

$$|Z_{C_E}| = \frac{1}{2\pi \cdot 1\mathrm{kHz}\cdot35\mu F} \approx 4.5 \Omega$$

at \$1\mathrm{kHz}\$ so your calculation of the gain isn't correct.

A more correct calculation of the gain at this frequency is

$$|A_v| = \left| \frac{R_C||R_L}{r_e + R_E||Z_{C_E}}\right| \approx 36.7  $$

According to the 'scope screen capture, the gain (magnitude) is about 33.5.

For your calculation to be correct, the capacitor impedance, at the frequencies of interest, must be much less than \$r_e\$.