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>

activepieces-fork/packages/pieces/community/posthog/src/i18n/ja.json

@@ -0,0 +1,51 @@
+{
+  "Open-source product analytics": "オープンソースの製品分析",
+  "\n[Click here](https://posthog.com/docs/api/overview#personal-api-keys-recommended) to learn how to obtain your Personal API key.\n": "\n[Click here](https://posthog.com/docs/api/overview#personal-api-keys-recommended) で、個人用APIキーの取得方法を学びます。\n",
+  "Create Event": "イベントを作成",
+  "Create Project": "プロジェクトを作成",
+  "Custom API Call": "カスタムAPI通話",
+  "Create an event inside a project": "プロジェクト内でイベントを作成する",
+  "Create a posthog project": "ポスログプロジェクトを作成",
+  "Make a custom API call to a specific endpoint": "特定のエンドポイントへのカスタム API コールを実行します。",
+  "Event name": "イベント名",
+  "Event type": "イベントの種類",
+  "Distinct Id": "個別ID",
+  "Properties": "プロパティー",
+  "Context": "コンテキスト",
+  "Message ID": "メッセージID",
+  "Category": "カテゴリ",
+  "Name": "Name",
+  "Slack Incoming Webhook": "Slack Incoming Webhook",
+  "Anonymize IPs": "IPの匿名化",
+  "Is demo project": "デモプロジェクト",
+  "Method": "方法",
+  "Headers": "ヘッダー",
+  "Query Parameters": "クエリパラメータ",
+  "Body": "本文",
+  "Response is Binary ?": "応答はバイナリですか?",
+  "No Error on Failure": "失敗時にエラーはありません",
+  "Timeout (in seconds)": "タイムアウト（秒）",
+  "The event name": "イベント名",
+  "User's Distinct Id": "User's Distinct Id",
+  "The event properties": "イベントのプロパティ",
+  "The event context,": "イベントのコンテキスト",
+  "The message id,": "メッセージ ID",
+  "The event category.": "イベントカテゴリ。",
+  "Project Name": "プロジェクト名",
+  "Slack incoming webhook": "WebhookをSlack incoming",
+  "Whether to anonymize incoming IP addresses.": "受信IPアドレスを匿名化するかどうかを設定します。",
+  "If this is a demo project": "デモプロジェクトの場合",
+  "Authorization headers are injected automatically from your connection.": "認証ヘッダは接続から自動的に注入されます。",
+  "Enable for files like PDFs, images, etc..": "PDF、画像などのファイルを有効にします。",
+  "Alias": "Alias",
+  "Capture": "Capture",
+  "Identify": "識別",
+  "Page": "ページ",
+  "Screen": "画面",
+  "GET": "取得",
+  "POST": "POST",
+  "PATCH": "PATCH",
+  "PUT": "PUT",
+  "DELETE": "削除",
+  "HEAD": "頭"
+}