docs: build OpenAPI spec and cut version 1.10 (#13537)

* build-api

* bump-version-to-1.10

* fix-broken-links

docs/versioned_docs/version-1.10.0/API-Reference/python-examples/api-flows-run/run-flow.py

@@ -0,0 +1,26 @@
+import os
+
+import requests
+
+base = os.environ.get("LANGFLOW_URL") or os.environ.get("LANGFLOW_SERVER_URL", "")
+flow_id = os.environ.get("FLOW_ID", "")
+api_key = os.environ.get("LANGFLOW_API_KEY", "")
+
+url = f"{base}/api/v1/run/{flow_id}"
+
+headers = {
+    "Content-Type": "application/json",
+    "x-api-key": api_key,
+}
+
+payload = {
+    "input_value": "Tell me about something interesting!",
+    "session_id": "chat-123",
+    "input_type": "chat",
+    "output_type": "chat",
+    "output_component": "",
+}
+
+response = requests.post(url, headers=headers, json=payload, timeout=60)
+response.raise_for_status()
+print(response.text)