Setting up HomeAssistant + ESPHome under docker?

Yes. This is where the yaml for devices you configured yourself are kept. If you have a Bluetooth proxy or voice assistant you configured using the website, they won’t be there.

If you want to be using the upgrade button in HA - I think there is some extra config you need. About halfway down in the first post of this thread is some config for pointing HA to your ESPHome docker container. I’ve never tried it so don’t know if it works.