chores(core): bump api-core dependency to 1.16.0 (#10111)

Author: jkwlui

core/setup.py

@@ -28,7 +28,7 @@
 # 'Development Status :: 4 - Beta'
 # 'Development Status :: 5 - Production/Stable'
 release_status = "Development Status :: 4 - Beta"
-dependencies = ["google-api-core >= 1.14.0, < 2.0.0dev"]
+dependencies = ["google-api-core >= 1.16.0, < 2.0.0dev"]
 extras = {"grpc": "grpcio >= 1.8.2, < 2.0dev"}