chore: update librarian to v0.20.0 (#13418)

Update librarian version to v0.20.0.
Also run `go run github.com/googleapis/librarian/cmd/librarian@${V}
tidy`.

For googleapis/librarian#6173

Author: zhumin8

.github/workflows/librarian_generation_check.yaml

@@ -57,7 +57,7 @@ jobs:
     - name: Run librarian install
       run: |
         librarian install
-        echo "$HOME/java_tools/bin" >> $GITHUB_PATH
+        echo "$HOME/.cache/librarian/bin/java_tools/bin" >> $GITHUB_PATH
     - name: Run librarian generate
       env:
         PYTHONPATH: ${{ github.workspace }}/sdk-platform-java/hermetic_build/library_generation/owlbot

.github/workflows/update_librarian_googleapis.yaml

@@ -116,7 +116,7 @@ jobs:
       if: steps.detect_librarian.outputs.has_changes == 'true'
       run: |
         go run github.com/googleapis/librarian/cmd/librarian@latest install
-        echo "$HOME/java_tools/bin" >> $GITHUB_PATH
+        echo "$HOME/.cache/librarian/bin/java_tools/bin" >> $GITHUB_PATH
       env:
         PYTHONPATH: ${{ github.workspace }}/sdk-platform-java/hermetic_build/library_generation/owlbot
     - name: Generate Libraries