Fix timeout middleware panic on proxy/WebSocket routes and worker healthcheck

The TimeoutMiddleware wraps the response writer in *http.timeoutWriter which
doesn't implement http.Flusher. When the admin reverse proxy or WebSocket
upgrader tries to flush, it panics and crashes the container (502 Bad Gateway).
Skip timeout for /admin, /_next, and /ws routes.

Also fix the Dockerfile HEALTHCHECK to detect the worker process — the worker
has no HTTP server so the curl-based check always failed, marking it unhealthy.

Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>

internal/router/router.go

@@ -4,6 +4,7 @@ import (
 	"errors"
 	"fmt"
 	"net/http"
+	"strings"
 	"time"
 
 	"github.com/go-playground/validator/v10"
@@ -60,6 +61,16 @@ func SetupRouter(deps *Dependencies) *echo.Echo {
 	e.Use(middleware.BodyLimit("1M")) // 1MB default for JSON payloads
 	e.Use(middleware.TimeoutWithConfig(middleware.TimeoutConfig{
 		Timeout: 30 * time.Second,
+		Skipper: func(c echo.Context) bool {
+			path := c.Request().URL.Path
+			// Skip timeout for reverse proxy and WebSocket routes — the
+			// timeout middleware wraps the response writer in *http.timeoutWriter
+			// which does not implement http.Flusher, causing a panic when
+			// httputil.ReverseProxy or WebSocket upgraders try to flush.
+			return strings.HasPrefix(path, "/admin") ||
+				strings.HasPrefix(path, "/_next") ||
+				strings.HasSuffix(path, "/ws")
+		},
 	}))
 	e.Use(corsMiddleware(cfg))
 	e.Use(i18n.Middleware())