Trying to cache android sdk or cmdline tools doesn't work due to invalid path warning while path exists

I'm working on a github actions workflow that installs comdline tools and sdk packages every run and I want to cache these directories

       - name: Restore Android SDK Cache
          uses: actions/cache@v3
          with:
           path: $HOME/android-sdk
           key: ${{ runner.os }}-android-sdk 

I get this warning in Post Restore Android SDK Cache step and nothing is cached even after first run:

Warning: Path Validation Error: Path(s) specified in the action for caching do(es) not exist, hence no cache is being saved.

this is the action where I download cmdline tools

      - name: Download Android Command Line Tools
        run: |
          set -e
          SDK_TOOLS_URL="https://dl.google.com/android/repository/commandlinetools-linux-8512546_latest.zip"

          mkdir -p $HOME/android-sdk/cmdline-tools
          curl -o sdk-tools.zip $SDK_TOOLS_URL
          unzip -q sdk-tools.zip -d $HOME/android-sdk/cmdline-tools
          mv $HOME/android-sdk/cmdline-tools/cmdline-tools $HOME/android-sdk/cmdline-tools/latest
          rm sdk-tools.zip
          echo "Setup completed. Directory structure:"
          tree $HOME/android-sdk/cmdline-tools || ls -R $HOME/android-sdk/cmdline-tools 

I have tried so many things and I tried to set the cache step before and after the download step but nothing works

Start with the actions/cache@v3 path input and the Download Android Command Line Tools step, checking the resolved directory after the download rather than only the configured string. Re-run the workflow and verify the post-cache step no longer reports the Path Validation Error and that a later run restores or saves the cache.