docs: update MCP connection states to include CONNECTED state and enum constants

This updates the documentation to reflect PR #672 which:
- Adds MCPConnectionState enum constants (AUTHENTICATING, CONNECTING, CONNECTED, DISCOVERING, READY, FAILED)
- Introduces new CONNECTED state in the connection state machine
- Improves type safety by providing enum-like constants instead of string literals

Updated files:
- Added new CONNECTED state to connection state type definitions
- Documented the MCPConnectionState constants with usage examples
- Updated OAuth guide with connection state flow including CONNECTED state
- Added examples showing enum constant usage for better type safety

🤖 Generated with [Claude Code](https://claude.com/claude-code)

Co-Authored-By: Claude <noreply@anthropic.com>

Author: github-actions[bot]

src/content/docs/agents/guides/oauth-mcp-client.mdx

@@ -201,7 +201,7 @@ export class MyAgent extends Agent<Env, never> {
 				([id, server]) => ({
 					serverId: id,
 					name: server.name,
-					state: server.state, // "authenticating" | "connecting" | "ready" | "failed"
+					state: server.state, // "authenticating" | "connecting" | "connected" | "discovering" | "ready" | "failed"
 					isReady: server.state === "ready",
 					needsAuth: server.state === "authenticating",
 					authUrl: server.auth_url,
@@ -220,7 +220,7 @@ export class MyAgent extends Agent<Env, never> {
 
 </TypeScriptExample>
 
-Connection states: `authenticating` (needs OAuth) > `connecting` (completing setup) > `ready` (available for use)
+Connection states: `authenticating` (needs OAuth) > `connecting` (establishing transport) > `connected` (transport established) > `discovering` (loading capabilities) > `ready` (available for use)
 
 ## Handle authentication failures
 
@@ -296,6 +296,59 @@ Common failure reasons:
 
 Failed connections remain in state until you remove them with `removeMcpServer(serverId)`.
 
+## Use connection state constants
+
+For better type safety, use the `MCPConnectionState` enum constants instead of string literals when checking connection states:
+
+<TypeScriptExample>
+
+```tsx title="src/App.tsx"
+import { useAgent, MCPConnectionState } from "agents/react";
+import type { MCPServersState } from "agents";
+
+function App() {
+	const [mcpState, setMcpState] = useState<MCPServersState>({
+		prompts: [],
+		resources: [],
+		servers: {},
+		tools: [],
+	});
+
+	const agent = useAgent({
+		agent: "my-agent",
+		name: "session-id",
+		onMcpUpdate: (mcpServers: MCPServersState) => {
+			setMcpState(mcpServers);
+		},
+	});
+
+	return (
+		<div>
+			{Object.entries(mcpState.servers).map(([id, server]) => (
+				<div key={id}>
+					<strong>{server.name}</strong>: {server.state}
+					{server.state === MCPConnectionState.AUTHENTICATING && server.auth_url && (
+						<button onClick={() => window.open(server.auth_url, "_blank")}>
+							Authorize
+						</button>
+					)}
+					{server.state === MCPConnectionState.FAILED && (
+						<button onClick={() => handleRetry(id)}>Retry</button>
+					)}
+					{server.state === MCPConnectionState.READY && (
+						<span>✓ Ready</span>
+					)}
+				</div>
+			))}
+		</div>
+	);
+}
+```
+
+</TypeScriptExample>
+
+Using constants prevents typos and provides better IDE autocomplete. See the [Connection State Constants](/agents/model-context-protocol/mcp-client-api/#connection-state-constants) section for the full list.
+
 ## Complete example
 
 This example demonstrates a complete Cloudflare Observability OAuth integration. Users connect to Cloudflare Observability, authorize in a popup window, and the connection becomes available. The Agent provides endpoints to connect, check status, and disconnect.

src/content/docs/agents/model-context-protocol/mcp-client-api.mdx

@@ -193,8 +193,9 @@ An `MCPServersState` object containing:
 			state:
 				| "authenticating"
 				| "connecting"
-				| "ready"
+				| "connected"
 				| "discovering"
+				| "ready"
 				| "failed";
 			capabilities: ServerCapabilities | null;
 			instructions: string | null;
@@ -228,7 +229,55 @@ export class MyAgent extends Agent<Env, never> {
 
 </TypeScriptExample>
 
-The `state` field can be: `authenticating`, `connecting`, `ready`, `discovering`, or `failed`. Use this method to monitor connection status, list available tools, or build UI for connected servers.
+The `state` field indicates the current connection state:
+
+- `authenticating` — Waiting for OAuth authorization to complete
+- `connecting` — Establishing transport connection to MCP server
+- `connected` — Transport connection established successfully
+- `discovering` — Discovering server capabilities (tools, resources, prompts)
+- `ready` — Fully connected and ready to use
+- `failed` — Connection failed at some point
+
+Use this method to monitor connection status, list available tools, or build UI for connected servers.
+
+## Connection State Constants
+
+The `MCPConnectionState` object provides enum-like constants for working with connection states:
+
+<TypeScriptExample>
+
+```ts title="src/index.ts"
+import { Agent, MCPConnectionState } from "agents";
+
+export class MyAgent extends Agent<Env, never> {
+	async onRequest(request: Request): Promise<Response> {
+		const mcpState = this.getMcpServers();
+
+		for (const [serverId, server] of Object.entries(mcpState.servers)) {
+			if (server.state === MCPConnectionState.READY) {
+				console.log(`Server ${serverId} is ready`);
+			} else if (server.state === MCPConnectionState.AUTHENTICATING) {
+				console.log(`Server ${serverId} needs authentication`);
+			}
+		}
+
+		return new Response("OK");
+	}
+}
+```
+
+</TypeScriptExample>
+
+Available constants:
+
+- `MCPConnectionState.AUTHENTICATING` — `"authenticating"`
+- `MCPConnectionState.CONNECTING` — `"connecting"`
+- `MCPConnectionState.CONNECTED` — `"connected"`
+- `MCPConnectionState.DISCOVERING` — `"discovering"`
+- `MCPConnectionState.READY` — `"ready"`
+- `MCPConnectionState.FAILED` — `"failed"`
+
+Using these constants instead of string literals provides better type safety and prevents typos.
 
 ## OAuth Configuration