chore: Update SDK documentation (#2604)

Co-authored-by: marvin-context-protocol[bot] <225465937+marvin-context-protocol[bot]@users.noreply.github.com>

docs/python-sdk/fastmcp-server-tasks-routing.mdx

@@ -0,0 +1,37 @@
+---
+title: routing
+sidebarTitle: routing
+---
+
+# `fastmcp.server.tasks.routing`
+
+
+Task routing helper for MCP components.
+
+Provides unified task mode enforcement and docket routing logic.
+
+
+## Functions
+
+### `check_background_task` <sup><a href="https://github.com/jlowin/fastmcp/blob/main/src/fastmcp/server/tasks/routing.py#L26" target="_blank"><Icon icon="github" style="width: 14px; height: 14px;" /></a></sup>
+
+```python
+check_background_task(component: Tool | Resource | ResourceTemplate | Prompt, task_type: TaskType, key: str, arguments: dict[str, Any] | None = None) -> mcp.types.CreateTaskResult | None
+```
+
+
+Check task mode and submit to background if requested.
+
+**Args:**
+- `component`: The MCP component
+- `task_type`: Type of task ("tool", "resource", "template", "prompt")
+- `key`: Docket registration key (caller resolves from contextvar + fallback)
+- `arguments`: Arguments for tool/prompt/template execution
+
+**Returns:**
+- CreateTaskResult if submitted to docket, None for sync execution
+
+**Raises:**
+- `McpError`: If mode="required" but no task metadata, or mode="forbidden"
+      but task metadata is present
+