[remote_base] Add Symphony IR protocol (encode/decode) with command_repeats support (#10777)

tests/components/remote_receiver/common-actions.yaml

@@ -143,6 +143,11 @@ on_sony:
     - logger.log:
         format: "on_sony: %lu %u"
         args: ["long(x.data)", "x.nbits"]
+on_symphony:
+  then:
+    - logger.log:
+        format: "on_symphony: 0x%lX %u"
+        args: ["long(x.data)", "x.nbits"]
 on_toshiba_ac:
   then:
     - logger.log:

tests/components/remote_transmitter/common-buttons.yaml

@@ -53,6 +53,12 @@ button:
       remote_transmitter.transmit_sony:
         data: 0xABCDEF
         nbits: 12
+  - platform: template
+    name: Symphony
+    on_press:
+      remote_transmitter.transmit_symphony:
+        data: 0xE88
+        nbits: 12
   - platform: template
     name: Panasonic
     on_press: