MNT CI and README maintenance

[mvdoc]

Summary

• Increase pytest step timeout from 10 to 20 minutes
• Remove TestPyPI publishing job and workflow_dispatch trigger from publish.yml
• Update Python version badge from 3.6+ to 3.10+
• Add codecov and PyPI badges to README
• Add manual trigger (workflow_dispatch) for gh-pages deployment

Test plan

• Verify run_tests.yml timeout is 20 minutes
• Verify publish.yml only triggers on release and publishes to PyPI only
• Verify README badges render correctly
• Verify build_docs.yml can be manually triggered to deploy to gh-pages