Since the ESP32S module is specified at 3.0 - 3.6V operation you absolutely need a battery with a voltage over 1.5V.
The Expressif design guide is worth reading, the implication is that the cpu will work down to 1.8V ….but not necessarily the whole module. For example the Flash is rated at a min 2.7V.
The only choice you have for a single cell is to use two Nickel-zinc (NiZn) batteries with a terminal voltage of 1.65V.
Nickel-zinc is similar to nickel-cadmium in that it uses an alkaline
electrolyte and a nickel electrode, but it differs in voltage; NiZn
provides 1.65V/cell rather than 1.20V, which NiCd and NiMH deliver.
NiZn charges at a constant current to 1.9V/cell and cannot take
trickle charge, also known as maintenance charge. The specific energy
is 100Wh/kg and can be cycled 200–300 times. NiZn has no heavy toxic
materials and can easily be recycled. Some packaging is available in
the AA cell format.
In 1901, Thomas Edison was awarded the U.S. patent for a rechargeable
nickel–zinc battery system that was installed in rail cars between
1932 and 1948. NiZn suffered from high self-discharge and short cycle
life caused by dendrite growth, which often led to an electrical
short. Improvements in the electrolyte have reduced this problem, and
NiZn is being considered again for commercial uses. Low cost, high
power output and good temperature operating range make this chemistry
Source: Battery University
You must take care when charging, since the terminal voltage can rise above 1.8V. If you fully charge them you will exceed the rating of your module. However you can charge them to a 1.8V terminal voltage without problem.
source: ANSMANN AA - 2500mWh NiZn battery Specification