my custom logic runs as something in home assistant usually, haven’t yet had a need to add stuff in the esphome config yet (although I could imagine many situations where it’s necessary)

Yeah, for sure. My more... uhh.. creative toys are definitely not ESPhome, but it's super cool that I can solder on a few wires to a DHT-11 and throw it in a closet with the weakest USB power plug I own, and end up with a great sensor.

You can definitely override existing and create custom C++ components in ESPHome without too much hassle. It allows lambdas in the YAML itself.