Serve MCP at a secret path, so claude.ai can connect

claude.ai's connector dialog takes a name and a URL. Sending a bearer token
needs a "Request headers" beta most accounts lack, and OAuth is not built
yet, so with MCP_PATH_SECRET set the endpoint is also served at
/<secret>/mcp without the bearer token — a trial until OAuth replaces it.

The path is the credential there. It is compared in constant time, and a
wrong one answers 404 like any unknown path. The config refuses fewer than 32
URL-safe characters and never echoes the value, nothing in the server logs
request paths, and the Caddy snippet rewrites the segment before an access
log entry is written (verified against Caddy 2.11). Claude Code and the CLI
keep the bearer token; DEPLOYMENT.md says what the path trades away.

178 tests. Smoke 76/76 and 74/74 on the local instance.

Co-Authored-By: Claude Opus 5 (1M context) <noreply@anthropic.com>

src/http/auth.ts

@@ -28,6 +28,26 @@ export function bearerAuth(expected: string) {
 	};
 }
 
+/**
+ * Gate for `/:secret/mcp`, the header-free way in.
+ *
+ * A wrong secret answers exactly like any other unknown path, so guessing
+ * learns nothing — not even that the route exists. The comparison is
+ * constant-time for the same reason as the bearer check's.
+ */
+export function pathSecret(expected: string) {
+	const expectedBytes = Buffer.from(expected, 'utf8');
+
+	return function checkPathSecret(req: Request, res: Response, next: NextFunction): void {
+		const presented = req.params.secret;
+		if (typeof presented !== 'string' || !constantTimeEquals(Buffer.from(presented, 'utf8'), expectedBytes)) {
+			res.status(404).json({ error: 'not_found' });
+			return;
+		}
+		next();
+	};
+}
+
 function extractToken(authorization: string | undefined, apiKey: string | undefined): string | undefined {
 	if (authorization) {
 		const match = /^Bearer\s+(.+)$/i.exec(authorization.trim());