feat(api): public API plan gating, docs auth, and dashboard snippets (#701)

* fix(automation): align public API plan gating across cloud and self-hosted

Add shared canUsePublicApi helper so cloud allows Early Adopter and
Enterprise while self-hosted requires Enterprise. Update the API key
dashboard page and backend key creation checks to use the same rules.

Co-authored-by: Rotimi Best <rotimi-best@users.noreply.github.com>

* docs(api): document bearer auth on public API reference

Add shared OpenAPI enrichment with bearerAuth security scheme and
authentication instructions. The interactive reference now loads an
enriched spec with Authorize support, and the API guide explains how
to create and use org API keys.

Co-authored-by: Rotimi Best <rotimi-best@users.noreply.github.com>

* feat(dashboard): add API quick-start code snippets on automation page

Mirror the MCP client setup section with cURL, JavaScript, and Python
examples that show how to authenticate public API requests with org keys.

Co-authored-by: Rotimi Best <rotimi-best@users.noreply.github.com>

* ci(openapi): republish spec when public API OpenAPI helpers change

Co-authored-by: Rotimi Best <rotimi-best@users.noreply.github.com>

* feat(dashboard): add Go snippet to API quick-start examples

Co-authored-by: Rotimi Best <rotimi-best@users.noreply.github.com>

* docs(api): use /org/*/api and clarify dashboard key generation path

Co-authored-by: Rotimi Best <rotimi-best@users.noreply.github.com>

* fix(api): escape backticks in OpenAPI description template literal

Greptile flagged that unescaped backticks around * in
PUBLIC_API_OPENAPI_DESCRIPTION evaluated to NaN and dropped auth docs
from the Scalar spec. Also use plan-specific snackbar message on upgrade.

Co-authored-by: Rotimi Best <rotimi-best@users.noreply.github.com>

---------

Co-authored-by: Cursor Agent <cursoragent@cursor.com>
Co-authored-by: Rotimi Best <rotimi-best@users.noreply.github.com>

apps/dashboard/src/lib/utils/translations/vi.json

@@ -503,7 +503,8 @@
     "download_lessons": "Nâng cấp để tải bài học",
     "download_course": "Nâng cấp để tải xuống khóa học",
     "required": "Yêu cầu nâng cấp",
-    "enterprise_required": "Tính năng này yêu cầu gói Enterprise."
+    "enterprise_required": "Tính năng này yêu cầu gói Enterprise.",
+    "public_api_required": "Nâng cấp lên Early Adopter hoặc Enterprise để truy cập API công khai."
   },
   "analytics": {
     "title": "Phân tích",
@@ -3892,6 +3893,10 @@
           "save": "Create key"
         }
       },
+      "setup": {
+        "title": "Bắt đầu nhanh",
+        "description": "Dùng khóa API làm Bearer token cho mọi yêu cầu. Thay chỗ giữ chỗ bằng khóa ở trên, hoặc dán secret ngay sau khi tạo khóa."
+      },
       "view_docs": "View Docs"
     },
     "keys": {
@@ -3916,7 +3921,11 @@
       "claude_code": "Mã Claude",
       "codex": "Codex",
       "cursor": "Con trỏ",
-      "opencode": "OpenCode"
+      "opencode": "OpenCode",
+      "curl": "cURL",
+      "javascript": "JavaScript",
+      "python": "Python",
+      "go": "Go"
     },
     "tabs": {
       "mcp": "MCP",