Help for stream homeassistant log event to oled display

Hi, someone know how to send homeassistant log event such as “Kitchen light now on” “User is at home” etc… to esphome?

I have a Oled display connected via i2c to a development board esp32 with esphome, my goal
would like to be to send all homeassistant event trough text sensor for showing on oled display in real time what happen but i cant find a valid method.
I did some tests with mqtt eventstream but i think doesn’t is the right way the output is very verbose and grab desired infos is a nightmare.
Can you suggest me some solution please?