Link to googleapis.dev documentation in READMEs. (#8705)

packages/google-cloud-dataproc/README.rst

@@ -19,7 +19,7 @@ Python Client for Google Cloud Dataproc API
 .. |compat_check_github| image:: https://python-compatibility-tools.appspot.com/one_badge_image?package=git%2Bgit%3A//github.com/googleapis/google-cloud-python.git%23subdirectory%3Ddataproc
    :target: https://python-compatibility-tools.appspot.com/one_badge_target?package=git%2Bgit%3A//github.com/googleapis/google-cloud-python.git%23subdirectory%3Ddataproc
 .. _Google Cloud Dataproc API: https://cloud.google.com/dataproc
-.. _Client Library Documentation: https://googleapis.github.io/google-cloud-python/latest/dataproc/index.html
+.. _Client Library Documentation: https://googleapis.dev/python/dataproc/latest
 .. _Product Documentation:  https://cloud.google.com/dataproc
 
 Quick Start
@@ -35,7 +35,7 @@ In order to use this library, you first need to go through the following steps:
 .. _Select or create a Cloud Platform project.: https://console.cloud.google.com/project
 .. _Enable billing for your project.: https://cloud.google.com/billing/docs/how-to/modify-project#enable_billing_for_a_project
 .. _Enable the Google Cloud Dataproc API.:  https://cloud.google.com/dataproc
-.. _Setup Authentication.: https://googleapis.github.io/google-cloud-python/latest/core/auth.html
+.. _Setup Authentication.: https://googleapis.dev/python/google-api-core/latest/auth.html
 
 Installation
 ~~~~~~~~~~~~