Spiro is correct … deep-sleep is misnamed. It is actually a power off and power on operation which you can see in the ESPHome Log taken from a USB or serial terminal. And mentioned in the Notes on ESPHome deep_sleep thread.
Fortunately global variables are stored in non-volatile RAM so are retained through the “sleep”.
I recall seeing in ESPHome docs some device which specifically advised against deep_sleep because it has to start the long calibration process each time. I wondered if it was BME280; but no, it was MAX17043 battery fuel gauge.
Note also that ESPHome is multi-threaded … meaning that measuring sensors thread starts before the on_boot thread has finished - which can cause initial values to be incorrect. You might need to wake for a while longer for the IAQ reading to stabilize.