ChatGPT tells me thats very likely Puya PY32F002A and that can be as cheap as $0.0682 a piece if you order 5000 and upwards, which should be fairly the case for a mass market vape.

Hearing the term microcontroller makes you feel like a lot of compute capacity is being wasted. This is what you get in that microcontroller-

Puya PY32F002A: Cortex-M0+, up to 24 MHz, up to 20 KB Flash, 3 KB SRAM, ADC, timers, I²C/SPI/USART; available in QFN20/TSSOP20.

Its basically a small battery, a display and a microcontroller to show you battery charge and vape fluid levels. Mostly ADC work and display.