Include ui_web API files in sky_engine. (flutter/engine#40846)

Include `ui_web` API files in sky_engine.

engine/src/flutter/lib/ui/dart_ui.gni

@@ -25,3 +25,10 @@ dart_ui_files = [
 ]
 
 dart_ui_path = "//flutter/lib/ui/ui.dart"
+
+dart_ui_web_files = [
+  "//flutter/lib/web_ui/lib/ui_web/src/ui_web/url_strategy.dart",
+  "//flutter/lib/web_ui/lib/ui_web/src/ui_web.dart",
+]
+
+dart_ui_web_path = "//flutter/lib/web_ui/lib/ui_web/src/ui_web.dart"

engine/src/flutter/sky/packages/sky_engine/BUILD.gn

@@ -175,6 +175,13 @@ copy("copy_dart_ui") {
   outputs = [ "$root_gen_dir/dart-pkg/sky_engine/lib/ui/{{source_file_part}}" ]
 }
 
+copy("copy_dart_ui_web") {
+  sources = dart_ui_web_files
+
+  outputs =
+      [ "$root_gen_dir/dart-pkg/sky_engine/lib/ui_web/{{source_file_part}}" ]
+}
+
 copy("copy_allowed_experiments") {
   sources = [ "//third_party/dart/sdk/lib/_internal/allowed_experiments.json" ]
 
@@ -230,6 +237,7 @@ generated_file("_embedder_yaml") {
     "  \"dart:math\": \"math/math.dart\"",
     "  \"dart:typed_data\": \"typed_data/typed_data.dart\"",
     "  \"dart:ui\": \"ui/ui.dart\"",
+    "  \"dart:ui_web\": \"ui_web/ui_web.dart\"",
     "",
     "  \"dart:_http\": \"_http/http.dart\"",
     "  \"dart:_interceptors\": \"_interceptors/interceptors.dart\"",
@@ -257,6 +265,7 @@ dart_pkg("sky_engine") {
     ":_embedder_yaml",
     ":copy_dart_sdk",
     ":copy_dart_ui",
+    ":copy_dart_ui_web",
   ]
 
   if (!is_fuchsia) {

engine/src/flutter/sky/packages/sky_engine/lib/_embedder.yaml

@@ -17,6 +17,7 @@ embedded_libs:
   "dart:math": "../../../../../third_party/dart/sdk/lib/math/math.dart"
   "dart:typed_data": "../../../../../third_party/dart/sdk/lib/typed_data/typed_data.dart"
   "dart:ui": "../../../../lib/ui/ui.dart"
+  "dart:ui_web": "../../../../lib/web_ui/lib/ui_web/src/ui_web.dart"
 
   "dart:_http": "../../../../../third_party/dart/sdk/lib/_http/http.dart"
   "dart:_interceptors": "../../../../../third_party/dart/sdk/lib/_interceptors/interceptors.dart"