Hi Michael,
A square-wave is not a problem. The maximum frequency we tested is 1kHz. But we only tested with square-wave signals generated by an Agilent 6811B generator which does not have steep slopes. The rating of 50V/nsec is a non-damage rating for the high-side drivers which is in line with normal power FETs. Proper functionality of the total IC at 50V/nsec is not relevant and not tested for a mains application which has an EMI_filter in front.
The 36Vpeak voltage is too close to the minimum voltage of 32V that is required for operation at 25C. Over temperature this will even need more than 32V. The TEA2208T is not intended for such low voltages. I would not recommend it.

Also note that that this is not a peak rectifier, but a full-wave rectifier. Looking at the picture below you see that a diode rectifier will output a DC voltage with ripple on it depending on the capacitor and the load current. With the TEA2208T you always get the full-wave rectified input, independent from capacitor or load current. If DC-voltage is required after the bridge, the TEA2208T should not be used.

Best regards,
Tomas