Improved Alexa ThermostatController thermostatMode handling (#28176)

* Update ThermostatController to map directives to supported modes and add support for CUSTOM mode.

* Removed erroneous config value from test.

* Removed unnecessary use of a comprehension by dumbing down comment so pylint could comprehend.

* Removed erroneous import variable caused by removing erroneous config value from test.

* Removed unnecessary use of a comprehension.

* Reverted Removal or erroneous import variable and erroneous config value from test.
Apparently need for additional tests outside this component. Whoops.

tests/components/alexa/test_capabilities.py

@@ -472,11 +472,7 @@ async def test_report_climate_state(hass):
             {"value": 34.0, "scale": "CELSIUS"},
         )
 
-    for off_modes in (
-        climate.HVAC_MODE_OFF,
-        climate.HVAC_MODE_FAN_ONLY,
-        climate.HVAC_MODE_DRY,
-    ):
+    for off_modes in (climate.HVAC_MODE_OFF, climate.HVAC_MODE_FAN_ONLY):
         hass.states.async_set(
             "climate.downstairs",
             off_modes,
@@ -495,6 +491,23 @@ async def test_report_climate_state(hass):
             {"value": 34.0, "scale": "CELSIUS"},
         )
 
+    # assert dry is reported as CUSTOM
+    hass.states.async_set(
+        "climate.downstairs",
+        "dry",
+        {
+            "friendly_name": "Climate Downstairs",
+            "supported_features": 91,
+            climate.ATTR_CURRENT_TEMPERATURE: 34,
+            ATTR_UNIT_OF_MEASUREMENT: TEMP_CELSIUS,
+        },
+    )
+    properties = await reported_properties(hass, "climate.downstairs")
+    properties.assert_equal("Alexa.ThermostatController", "thermostatMode", "CUSTOM")
+    properties.assert_equal(
+        "Alexa.TemperatureSensor", "temperature", {"value": 34.0, "scale": "CELSIUS"}
+    )
+
     hass.states.async_set(
         "climate.heat",
         "heat",