[cloud functions] Update cloud functions to use NodeJS 10

Change-Id: Id54f47b5e7990643be01896bf3f7eedbecd8ec29
Reviewed-on: https://dart-review.googlesource.com/c/dart_ci/+/167780
Reviewed-by: Alexander Thomas <athom@google.com>
diff --git a/functions/build.yaml b/functions/build.yaml
index 88a03a3..1122fde 100644
--- a/functions/build.yaml
+++ b/functions/build.yaml
@@ -3,6 +3,7 @@
     sources:
       - "node/**"
       - "lib/**"
+      - "$package$"
     builders:
       build_node_compilers|entrypoint:
         generate_for:
diff --git a/functions/package.json b/functions/package.json
index dbe552e..e72b67d 100644
--- a/functions/package.json
+++ b/functions/package.json
@@ -10,11 +10,11 @@
     "logs": "firebase functions:log"
   },
   "engines": {
-    "node": "8"
+    "node": "10"
   },
   "dependencies": {
     "firebase-admin": "^8.10.0",
-    "firebase-functions": "^3.6.0"
+    "firebase-functions": "^3.6.1"
   },
   "private": true
 }