Refactor vehicle beacon configs and clean up gate

Extract shared M5ATOM vehicle code (esp32, on_loop, LED effects) into
common/vehicle_base.yaml, reducing each vehicle file from ~136 to 20
lines. Remove dead commented-out code from on_loop lambda.

Gate: fix on_multi_click and select indentation, change
esp32_ble_tracker id from ${name} to ${device} (lowercase),
remove unused commented-out gate_flash GPIO sensor.

Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>

mcu-vehicle-toyota-auris-ts.yaml

@@ -16,69 +16,12 @@ esphome:
             - binary_sensor.is_off: button
           then:
             - wifi.disable:
-  on_loop:
-    then:
-      lambda: |-
-        static uint32_t last_state = 0;
-        auto state = App.get_app_state();
-        if (state != last_state) {
-          if (state & STATUS_LED_ERROR) {
-            auto call = id(led).turn_on();
-            call.set_effect("ERROR");
-            call.perform();
-          } else if (state & STATUS_LED_WARNING) {
-            auto call = id(led).turn_on();
-            call.set_effect("BOOT");
-            call.perform();
-          } else {
-            //auto call = id(led).turn_off();
-            //call.perform();
-            auto call = id(led).turn_on();
-            call.set_effect("BEACON");
-            call.perform();
-          }
-          last_state = state;
-        }
-
-esp32:
-  variant: esp32
-  framework:
-    type: esp-idf
-    # version: 5.3.2
-    # platform_version: 53.03.11
-
-external_components:
-  - source: components
 
 packages:
+  base: !include common/vehicle_base.yaml
   wifi: !include common/wifi.yaml
   logger: !include common/logger.yaml
-  # api: !include common/api.yaml
   ota: !include common/ota.yaml
-#   common: !include common/common.yaml
-
-# api:
-#   reboot_timeout: 0s
-
-# wifi:
-#   enable_on_boot: false
-
-# debug:
-
-# PINOUTS: M5ATOM
-# IR        G12
-# NEO       G27
-# BUTTON    G39
-# I2C0 SDA  G26
-# I2C0 SCL  G32
-# I2C1 SDA  G25
-# I2C1 SCL  G21
-# UART0 RX  G3
-# UART0 TX  G1
-# UART1 RX  G23
-# UART1 TX  G33
-# 1-WIRE    G22
-# NC        G19
 
 binary_sensor:
   - platform: gpio
@@ -92,63 +35,3 @@ esp32_ble_beacon:
   uuid: !secret ble_beacon_toyota_auris_uuid
   major: !secret ble_beacon_toyota_auris_major
   minor: !secret ble_beacon_toyota_auris_minor
-
-light:
-  - platform: esp32_rmt_led_strip
-    name: LED
-    id: led
-    rgb_order: GRB
-    pin: 27
-    num_leds: 1
-    chipset: ws2812
-    restore_mode: ALWAYS_OFF
-    effects:
-      - strobe:
-          name: "BEACON"
-          colors:
-            - state: true
-              red: 0%
-              green: 0%
-              blue: 50%
-              duration: 200ms
-            - state: false
-              duration: 200ms
-            - state: true
-              red: 0%
-              green: 0%
-              blue: 50%
-              duration: 200ms
-            - state: false
-              duration: 10s
-      - lambda:
-          name: "ERROR"
-          update_interval: 0.5s
-          lambda: |-
-            static bool state = false;
-            auto call = id(led).turn_on();
-            call.set_transition_length(500);
-            call.set_rgb(1, 0, 0);
-            if (!state) {
-              call.set_brightness(1);
-            } else {
-              // If using 0, it freaks Home Assistant UI.
-              call.set_brightness(0.01);
-            }
-            call.perform();
-            state = !state;
-      - lambda:
-          name: "BOOT"
-          update_interval: 0.5s
-          lambda: |-
-            static bool state = false;
-            auto call = id(led).turn_on();
-            call.set_transition_length(500);
-            call.set_rgb(0, 1, 0);
-            if (!state) {
-              call.set_brightness(1);
-            } else {
-              // If using 0, it freaks Home Assistant UI.
-              call.set_brightness(0.01);
-            }
-            call.perform();
-            state = !state;