Fix flaky test_api_conditional_memory and improve integration test patterns (#9379)

tests/integration/fixtures/api_conditional_memory.yaml

@@ -2,14 +2,10 @@ esphome:
   name: api-conditional-memory-test
 host:
 api:
-  batch_delay: 0ms
   actions:
     - action: test_simple_service
       then:
         - logger.log: "Simple service called"
-        - binary_sensor.template.publish:
-            id: service_called_sensor
-            state: ON
     - action: test_service_with_args
       variables:
         arg_string: string
@@ -20,53 +16,14 @@ api:
         - logger.log:
             format: "Service called with: %s, %d, %d, %.2f"
             args: [arg_string.c_str(), arg_int, arg_bool, arg_float]
-        - sensor.template.publish:
-            id: service_arg_sensor
-            state: !lambda 'return arg_float;'
   on_client_connected:
     - logger.log:
         format: "Client %s connected from %s"
         args: [client_info.c_str(), client_address.c_str()]
-    - binary_sensor.template.publish:
-        id: client_connected
-        state: ON
-    - text_sensor.template.publish:
-        id: last_client_info
-        state: !lambda 'return client_info;'
   on_client_disconnected:
     - logger.log:
         format: "Client %s disconnected from %s"
         args: [client_info.c_str(), client_address.c_str()]
-    - binary_sensor.template.publish:
-        id: client_connected
-        state: OFF
-    - binary_sensor.template.publish:
-        id: client_disconnected_event
-        state: ON
 
 logger:
   level: DEBUG
-
-binary_sensor:
-  - platform: template
-    name: "Client Connected"
-    id: client_connected
-    device_class: connectivity
-  - platform: template
-    name: "Client Disconnected Event"
-    id: client_disconnected_event
-  - platform: template
-    name: "Service Called"
-    id: service_called_sensor
-
-sensor:
-  - platform: template
-    name: "Service Argument Value"
-    id: service_arg_sensor
-    unit_of_measurement: ""
-    accuracy_decimals: 2
-
-text_sensor:
-  - platform: template
-    name: "Last Client Info"
-    id: last_client_info