Add UMA metric: Startup.BrowserMainToRendererMain.

components/startup_metric_utils/browser/BUILD.gn

Index: components/startup_metric_utils/browser/BUILD.gn
diff --git a/components/startup_metric_utils/browser/BUILD.gn b/components/startup_metric_utils/browser/BUILD.gn
index 258e2106499354b071c22df473727e0a1e51d4a2..a40e1a327bebe79371dcaee883c38e5f117b58e6 100644
--- a/components/startup_metric_utils/browser/BUILD.gn
+++ b/components/startup_metric_utils/browser/BUILD.gn
@@ -2,6 +2,10 @@
 # Use of this source code is governed by a BSD-style license that can be
 # found in the LICENSE file.
 
+# We have 2 separate targets because //components/html_viewer requires :browser,
+# but has symbols that conflict with mojo symbols that :message_filter
+# indirectly depends on.
+
 source_set("browser") {
   sources = [
     "startup_metric_utils.cc",
@@ -12,3 +16,17 @@ source_set("browser") {
     "//base",
   ]
 }
+
+source_set("message_filter") {
+  sources = [
+    "startup_metric_message_filter.cc",
+    "startup_metric_message_filter.h",
+  ]
+
+  deps = [
+    ":browser",
+    "//base",
+    "//components/startup_metric_utils/common",
+    "//content/public/browser",
+  ]
+}