feat(web): mode-aware backlog banner — stop telling manual users summaries auto-arrive

The first pilot user sat in Manual mode reading "new summaries land gradually,
check back tomorrow" — copy that only makes sense in Automatic mode. Manual mode
never auto-summarizes, so the banner promised delivery that would never come.

The list page now reads the user's summarize mode and shows mode-correct copy:
- Auto: unchanged "land gradually" backlog note.
- Manual: "new videos appear here but are not summarized automatically — use the
  Summarize button" plus a "Switch to Automatic" link to /account.
The connected-but-empty first-run state is likewise mode-aware.

Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>

internal/web/handlers_test.go

@@ -477,3 +477,36 @@ func postAction(t *testing.T, app *web.App, videoID, action string, htmx bool) *
 	}
 	return do(t, app, req)
 }
+
+// TestListManualModeBannerCopy: a manual-mode user with un-summarized videos
+// sees the manual prompt (click Summarize), NOT the "summaries land
+// automatically" copy that misled the first pilot user into waiting forever.
+func TestListManualModeBannerCopy(t *testing.T) {
+	ctx := context.Background()
+	app := newApp(t)
+	p := rawPool(t)
+	resetDB(t, p)
+	seedVideo(t, p, videoX, "X Title", "https://x", time.Time{}) // pending, un-summarized
+	require.NoError(t, app.Store.SetAutoSummarize(ctx, userID, false))
+
+	html := body(t, do(t, app, httptest.NewRequest(http.MethodGet, "/", nil)))
+	require.Contains(t, html, "Manual mode")
+	require.Contains(t, html, "are not summarized automatically")
+	require.NotContains(t, html, "land gradually",
+		"manual-mode user must not be told summaries arrive automatically")
+}
+
+// TestListAutoModeBannerCopy: an auto-mode user with a backlog sees the
+// gradual-delivery copy, not the manual prompt.
+func TestListAutoModeBannerCopy(t *testing.T) {
+	ctx := context.Background()
+	app := newApp(t)
+	p := rawPool(t)
+	resetDB(t, p)
+	seedVideo(t, p, videoX, "X Title", "https://x", time.Time{})
+	require.NoError(t, app.Store.SetAutoSummarize(ctx, userID, true))
+
+	html := body(t, do(t, app, httptest.NewRequest(http.MethodGet, "/", nil)))
+	require.Contains(t, html, "land gradually")
+	require.NotContains(t, html, "are not summarized automatically")
+}