Add a context variable holding a HomeAssistant reference (#76303)

* Add a context variable holding a HomeAssistant reference

* Move variable setup and update test

* Refactor

* Revert "Refactor"

This reverts commit 346d005ee67b9e27e05363d04a7f48eaf416a16b.

* Set context variable when creating HomeAssistant object

* Update docstring

* Update docstring

Co-authored-by: jbouwh <jan@jbsoft.nl>