I'm using NiMH rechargeable AA-s. The LDO will get hotter with alkaline batteries, have not tried that. However, it behaves nicely when the input battery voltage goes below 3.3V, the output voltage follows the input.
The buttons are for GPIO0 and reset (flashing new software). To the right is the serial - USB converter.
Board with ESP-01 and serial - USB converter:
Naked board: