ESPHome is a platform developed for ESP32/ESP8266 and is mainly used for Smart Home devices. ESPHome has tons of ready made configurations, libraries and examples. In 2021 Nabu Casa (Home Assistant developer company) acquired ESPHome and integrated the whole ESPHome system more deep into the Home Assistant Core. These days ESPHome can be installed directly from Home Assistant Add-On store and configured from Home Assistant UI!
Bluetooth Proxy is a gateway software that listens for ‘all’ Bluetooth traffic and forwards them to the Home Assistant instance. Basically BLE to WiFi gateway.
Read more here;
https://blog.kastanis.gr/m5stack-atom-s3-lite-with-esphome/
https://esphome.io/guides/getting_started_hassio
https://esphome.io/components/wifi.html#configuration-variables