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.
It's still one or more PCBs, a battery, the LCD, the microphones, the microcontroller and the small components on the board. The capacity of the chip is besides the point. Each one of those components has a very deep production chain and cost a lot of resources to produce. ICs are created through chemical processes that use a bunch of substances that are themselves not manufactured, for example. The bottom line is, those electronics are wasteful.