Powering an esp32cam by a battery
The official ESP32-CAM has a AMS1117 voltage regulator that creates the 3.3V for the ESP.
The AMS1117 has an Absolute Maximum Input Voltage of 15V. It has a Dropout Voltage of 1.1-1.3V.
So you should stay above 4.6V to be on the safe side.
Since it's a linear voltage regulator, using a higher voltage battery has no advantage, as the &quot;excess voltage&quot; is converted to heat. It could even damage the regulator if too much heat is created.
You should pick the battery with the lowest voltage that still produces 4.6V when almost empty. So you could use the 7.3V battery you indicated. I'm assuming this is a 2-cell Li-ion battery, that has a voltage of 8.4V when full, and around 6V when empty. Which nicely fits your requirements.