Restart btproxy if no scan within 10 minutes

Mitigates https://github.com/esphome/issues/issues/6701

templates/btproxy.yaml

@@ -22,11 +22,19 @@ esp32_ble_tracker:
       - sensor.template.publish:
           id: ble_scans_finished
           state: !lambda 'return ++id(ble_scans);'
+      - script.execute: restart_after_delay
 
 bluetooth_proxy:
   id: btproxy
   active: true
 
+script:
+  - id: restart_after_delay
+    mode: restart
+    then:
+      - delay: 10min
+      - button.press: restart_button
+
 sensor:
   - platform: template
     name: "btproxy connections free"

templates/restart.yaml

@@ -2,3 +2,4 @@ button:
 - platform: restart
   name: "ESP chip restart"
   entity_category: diagnostic
+  id: restart_button