ci(docs-infra): split `test_and_deploy_aio` to two separate jobs (#26746)

By splitting the jobs, if something goes wrong with deploying (e.g. a
network issue), we can re-run just that part instead of having to wait
for all the tests to complete again.

In terms of total duration, the difference should be minimal, because
the two operations (testing and deploying) do not depend on shared
tasks. For example, we need to build again (for the specific target
environment; e.g. stable, next, etc.) before deploying anyway.

PR Close #26746

.circleci/config.yml

@@ -154,7 +154,7 @@ jobs:
       - *setup_bazel_remote_execution
       - run: bazel test //... --define=compile=aot --build_tag_filters=ivy-aot --test_tag_filters=ivy-aot
 
-  test_and_deploy_aio:
+  test_aio:
     <<: *job_defaults
     steps:
       - *define_env_vars
@@ -180,6 +180,15 @@ jobs:
       - run: xvfb-run --auto-servernum yarn --cwd aio e2e
         # Run unit tests for Firebase redirects
       - run: yarn --cwd aio redirects-test
+
+  deploy_aio:
+    <<: *job_defaults
+    steps:
+      - *define_env_vars
+      - checkout:
+          <<: *post_checkout
+      - restore_cache:
+          key: *cache_key
         # Deploy angular.io to production (if necessary)
       - run: echo "export CI_STABLE_BRANCH=$(npm info @angular/core dist-tags.latest | sed -r 's/^\s*([0-9]+\.[0-9]+)\.[0-9]+.*$/\1.x/')" | tee -a $BASH_ENV
       - run: xvfb-run --auto-servernum yarn --cwd aio deploy-production
@@ -388,7 +397,10 @@ workflows:
       - test_ivy_jit
       - test_ivy_aot
       - build-packages-dist
-      - test_and_deploy_aio
+      - test_aio
+      - deploy_aio:
+          requires:
+            - test_aio
       - test_aio_local:
           requires:
             - build-packages-dist