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/en.json

@@ -3963,7 +3963,8 @@
     "download_lessons": "Upgrade to download lessons",
     "download_course": "Upgrade to download course",
     "required": "Upgrade Required",
-    "enterprise_required": "This feature requires an Enterprise plan."
+    "enterprise_required": "This feature requires an Enterprise plan.",
+    "public_api_required": "Upgrade to Early Adopter or Enterprise to access the public API."
   },
   "automation": {
     "title": "Automation",
@@ -3982,7 +3983,11 @@
       "claude_code": "Claude Code",
       "codex": "Codex",
       "cursor": "Cursor",
-      "opencode": "OpenCode"
+      "opencode": "OpenCode",
+      "curl": "cURL",
+      "javascript": "JavaScript",
+      "python": "Python",
+      "go": "Go"
     },
     "keys": {
       "active": "Active",
@@ -4056,6 +4061,10 @@
           "save": "Create key"
         }
       },
+      "setup": {
+        "title": "Quick start",
+        "description": "Use your API key as a Bearer token on every request. Replace the placeholder with a key from above, or paste the secret immediately after you generate one."
+      },
       "view_docs": "View Docs"
     },
     "zapier": {