Increase HTTP client timeout values in client.py and update example in README.md.

Author: rodion-m

README.md

@@ -683,7 +683,7 @@ npm install -g mcp-remote
       "headers": {
         "Authorization": "Bearer YOUR_API_KEY_HERE"
       },
-      "timeout": 60000
+      "timeout": 310000
     }
   }
 }

src/core/client.py

@@ -68,7 +68,7 @@ async def codealive_lifespan(server: FastMCP) -> AsyncIterator[CodeAliveContext]
                 "Authorization": f"Bearer {config.api_key}",
                 "Content-Type": "application/json",
             },
-            timeout=60.0,
+            timeout=300.0,
             verify=config.verify_ssl,
         )
     else:
@@ -78,7 +78,7 @@ async def codealive_lifespan(server: FastMCP) -> AsyncIterator[CodeAliveContext]
             headers={
                 "Content-Type": "application/json",
             },
-            timeout=60.0,
+            timeout=300.0,
             verify=config.verify_ssl,
         )