ci: improve GitHub Actions workflow with caching and Docker build

[haosenwang1018]

Summary

Improves the CI workflow to provide faster feedback and better coverage.

Changes

• Separate lint job: Runs shell linting in parallel for faster feedback
• Add pip caching: Caches Python dependencies to speed up test runs
• Add Docker build job: Verifies Dockerfile builds correctly
• Use Docker Buildx: Enables layer caching for Docker builds
• Lint all shell scripts: Checks all .sh files, not just run_loop.sh
• Verify install.sh: Adds syntax check for the install script

Benefits

• Faster CI runs with pip caching
• Earlier detection of shell script issues
• Ensures Docker image always builds
• Better organized job structure

Testing

• Workflow syntax validated
• No breaking changes to existing jobs