Add Activepieces integration for workflow automation

- Add Activepieces fork with SmoothSchedule custom piece
- Create integrations app with Activepieces service layer
- Add embed token endpoint for iframe integration
- Create Automations page with embedded workflow builder
- Add sidebar visibility fix for embed mode
- Add list inactive customers endpoint to Public API
- Include SmoothSchedule triggers: event created/updated/cancelled
- Include SmoothSchedule actions: create/update/cancel events, list resources/services/customers

🤖 Generated with [Claude Code](https://claude.com/claude-code)

Co-Authored-By: Claude Opus 4.5 <noreply@anthropic.com>

frontend/src/i18n/locales/en.json

@@ -22,6 +22,23 @@
     "hoursAgo": "{{count}}h ago",
     "daysAgo": "{{count}}d ago"
   },
+  "automations": {
+    "title": "Automations",
+    "subtitle": "Build powerful workflows to automate your business",
+    "loading": "Loading automation builder...",
+    "loadingBuilder": "Loading workflow builder...",
+    "builderTitle": "Automation Builder",
+    "aiEnabled": "AI Copilot Enabled",
+    "openInTab": "Open in new tab",
+    "locked": {
+      "title": "Automations",
+      "description": "Upgrade your plan to access powerful workflow automation with AI-powered flow creation."
+    },
+    "error": {
+      "title": "Unable to load automation builder",
+      "description": "There was a problem connecting to the automation service. Please try again."
+    }
+  },
   "common": {
     "loading": "Loading...",
     "error": "Error",
@@ -33,6 +50,7 @@
     "delete": "Delete",
     "edit": "Edit",
     "create": "Create",
+    "creating": "Creating...",
     "update": "Update",
     "close": "Close",
     "confirm": "Confirm",
@@ -1467,7 +1485,41 @@
     "pendingRequests": "Pending Requests",
     "noPendingRequests": "No pending requests",
     "dropToArchive": "Drop here to archive",
-    "min": "min"
+    "min": "min",
+    "scheduleAppointment": "Schedule Appointment",
+    "saveChanges": "Save Changes",
+    "cancel": "Cancel",
+    "createAppointment": "Create Appointment",
+    "unassigned": "Unassigned",
+    "notesPlaceholder": "Add notes about this appointment...",
+    "scheduleDetails": "Schedule Details"
+  },
+  "participants": {
+    "title": "Participants",
+    "additionalParticipants": "Additional Participants",
+    "addParticipant": "Add Participant",
+    "addStaff": "Add Staff",
+    "addCustomer": "Add Customer",
+    "addObserver": "Add Observer",
+    "addExternalEmail": "Add by Email",
+    "searchPlaceholder": "Search by name or email...",
+    "sendCalendarInvites": "Send calendar invitations",
+    "externalEmail": "External Email",
+    "name": "Name",
+    "email": "Email",
+    "noParticipants": "No participants added",
+    "removeParticipant": "Remove participant",
+    "roles": {
+      "STAFF": "Staff",
+      "CUSTOMER": "Customer",
+      "OBSERVER": "Observer",
+      "RESOURCE": "Resource"
+    },
+    "external": "External",
+    "emailRequired": "Email is required",
+    "invalidEmail": "Invalid email address",
+    "participantAdded": "Participant added",
+    "participantRemoved": "Participant removed"
   },
   "customers": {
     "title": "Customers",