Fix remaining github action environment failure issue (#3857)

Issues and solution detailed in the links below.

https://github.blog/changelog/2020-10-01-github-actions-deprecating-set-env-and-add-path-commands/
https://docs.github.com/en/free-pro-team@latest/actions/reference/workflow-commands-for-github-actions#setting-an-environment-variable
diff --git a/.github/workflows/publish_docs.yml b/.github/workflows/publish_docs.yml
index 05b097d..4f9dad2 100644
--- a/.github/workflows/publish_docs.yml
+++ b/.github/workflows/publish_docs.yml
@@ -54,8 +54,8 @@
           # top directory.
           mv -f docs/index.md .
           git add docs/ index.md
-          echo "::set-env name=has_diff::false"
-          git diff --cached --exit-code || echo "::set-env name=has_diff::true"
+          echo "has_diff=false" >> $GITHUB_ENV
+          git diff --cached --exit-code || echo "has_diff=true" >> $GITHUB_ENV
       - name: Committing updates
         if: env.has_diff == 'true'
         run: |
diff --git a/.github/workflows/update_llvm_dependent_submodules.yml b/.github/workflows/update_llvm_dependent_submodules.yml
index aa9c3fa..bd35404 100644
--- a/.github/workflows/update_llvm_dependent_submodules.yml
+++ b/.github/workflows/update_llvm_dependent_submodules.yml
@@ -37,10 +37,10 @@
       - name: Updating submodules
         run: ./scripts/git/update_to_llvm_syncpoint.py
       - name: Calculating SHAs
-        run: |
-          echo "::set-env name=LLVM_SHA::$(git submodule status third_party/llvm-project | awk '{print $1}' | cut -c -12)"
-          echo "::set-env name=TF_SHA::$(git submodule status third_party/tensorflow | awk '{print $1}' | cut -c -12)"
-          echo "::set-env name=LLVM_BAZEL_SHA::$(git submodule status third_party/llvm-bazel | awk '{print $1}' | cut -c -12)"
+        run:
+          echo "LLVM_SHA=$(git submodule status third_party/llvm-project | awk '{print $1}' | cut -c -12)" >> $GITHUB_ENV
+          echo "TF_SHA=$(git submodule status third_party/tensorflow | awk '{print $1}' | cut -c -12)" >> $GITHUB_ENV
+          echo "LLVM_BAZEL_SHA=$(git submodule status third_party/llvm-bazel | awk '{print $1}' | cut -c -12)" >> $GITHUB_ENV
       - name: Creating Pull Request
         uses: peter-evans/create-pull-request@v2
         with: