chore(python): push cloud library docs to staging bucket for Cloud RAD (#295)

Source-Link: https://github.com/googleapis/synthtool/commit/7fd61f8efae782a7cfcecc599faf52f9737fe584
Post-Processor: gcr.io/cloud-devrel-public-resources/owlbot-python:latest@sha256:4ee57a76a176ede9087c14330c625a71553cf9c72828b2c0ca12f5338171ba60

Co-authored-by: Owl Bot <gcf-owl-bot[bot]@users.noreply.github.com>
diff --git a/.github/.OwlBot.lock.yaml b/.github/.OwlBot.lock.yaml
index 7d98291..108063d 100644
--- a/.github/.OwlBot.lock.yaml
+++ b/.github/.OwlBot.lock.yaml
@@ -1,3 +1,3 @@
 docker:
   image: gcr.io/cloud-devrel-public-resources/owlbot-python:latest
-  digest: sha256:58f73ba196b5414782605236dd0712a73541b44ff2ff4d3a36ec41092dd6fa5b
+  digest: sha256:4ee57a76a176ede9087c14330c625a71553cf9c72828b2c0ca12f5338171ba60
diff --git a/.kokoro/docs/common.cfg b/.kokoro/docs/common.cfg
index 4847856..48e8985 100644
--- a/.kokoro/docs/common.cfg
+++ b/.kokoro/docs/common.cfg
@@ -30,7 +30,9 @@
 
 env_vars: {
     key: "V2_STAGING_BUCKET"
-    value: "docs-staging-v2"
+    # Push non-cloud library docs to `docs-staging-v2-staging` instead of the
+    # Cloud RAD bucket `docs-staging-v2`
+    value: "docs-staging-v2-staging"
 }
 
 # It will upload the docker image after successful builds.