Move ESPHomeManager into its own file (#95870)

* Move ESPHomeManager into its own file

This is not a functional change. This is only a reorganization
ahead of some more test coverage being added so moving tests
around can be avoided later.

* relos

* fixes

* merge a portion of new cover since its small and allows us to remove the __init__ from .coveragerc

.coveragerc

@@ -304,10 +304,10 @@ omit =
     homeassistant/components/escea/__init__.py
     homeassistant/components/escea/climate.py
     homeassistant/components/escea/discovery.py
-    homeassistant/components/esphome/__init__.py
     homeassistant/components/esphome/bluetooth/*
     homeassistant/components/esphome/domain_data.py
     homeassistant/components/esphome/entry_data.py
+    homeassistant/components/esphome/manager.py
     homeassistant/components/etherscan/sensor.py
     homeassistant/components/eufy/*
     homeassistant/components/eufylife_ble/__init__.py