fix(server): serve pprof profiles when a BaseURL is configured

net/http/pprof's Index resolves the profile name by trimming "/debug/pprof/" from
the raw request path, which never matches once MountRouter prepends the BasePath.
Requests for any profile without an explicit chi route fell through to the index
page, returning HTML with a 200 instead of the profile. The handler now strips the
BasePath first.

cmd/root.go

@@ -2,6 +2,7 @@ package cmd
 
 import (
 	"context"
+	"net/http"
 	"os"
 	"os/signal"
 	"strings"
@@ -138,7 +139,7 @@ func startServer(ctx context.Context) func() error {
 			a.MountRouter("Prometheus metrics", conf.Server.Prometheus.MetricsPath, p.GetHandler())
 		}
 		if conf.Server.DevEnableProfiler {
-			a.MountRouter("Profiling", "/debug", middleware.Profiler())
+			a.MountRouter("Profiling", "/debug", profilerHandler())
 		}
 		if strings.HasPrefix(conf.Server.UILoginBackgroundURL, "/") {
 			a.MountRouter("Background images", conf.Server.UILoginBackgroundURL, backgrounds.NewHandler())
@@ -147,6 +148,12 @@ func startServer(ctx context.Context) func() error {
 	}
 }
 
+// profilerHandler returns the pprof handler. net/http/pprof resolves the profile
+// name from the raw request path, so the BasePath has to come off first.
+func profilerHandler() http.Handler {
+	return http.StripPrefix(conf.Server.BasePath, middleware.Profiler())
+}
+
 // schedulePeriodicScan schedules a periodic scan of the music library, if configured.
 func schedulePeriodicScan(ctx context.Context) func() error {
 	return func() error {

cmd/root_test.go

@@ -0,0 +1,45 @@
+package cmd
+
+import (
+	"net/http"
+	"net/http/httptest"
+	"path"
+	"runtime/pprof"
+
+	"github.com/go-chi/chi/v5"
+	"github.com/navidrome/navidrome/conf"
+	"github.com/navidrome/navidrome/conf/configtest"
+	. "github.com/onsi/ginkgo/v2"
+	. "github.com/onsi/gomega"
+)
+
+var _ = Describe("profilerHandler", func() {
+	// Mirrors how server.MountRouter mounts the handler.
+	mount := func() http.Handler {
+		router := chi.NewRouter()
+		router.Mount(path.Join(conf.Server.BasePath, "/debug"), profilerHandler())
+		return router
+	}
+
+	BeforeEach(func() {
+		DeferCleanup(configtest.SetupConfig())
+		if pprof.Lookup("nd-profiler-test") == nil {
+			pprof.NewProfile("nd-profiler-test")
+		}
+	})
+
+	DescribeTable("serves a named profile",
+		func(basePath string) {
+			conf.Server.BasePath = basePath
+
+			w := httptest.NewRecorder()
+			target := path.Join(basePath, "/debug/pprof/nd-profiler-test") + "?debug=1"
+			mount().ServeHTTP(w, httptest.NewRequest(http.MethodGet, target, nil))
+
+			Expect(w.Code).To(Equal(http.StatusOK))
+			Expect(w.Body.String()).To(HavePrefix("nd-profiler-test profile: total 0"))
+		},
+		Entry("without a BasePath", ""),
+		Entry("with a BasePath", "/music"),
+	)
+})