Use fork's claude-code-base-action with critical fix

fix latest commit of base action

Update claude-code-base-action to commit with critical fix

🤖 Generated with [Claude Code](https://claude.ai/code)

Co-Authored-By: Claude <noreply@anthropic.com>

Update claude-code-base-action to latest OAuth-supporting commit

Update action.yml

Release v0.0.13 - OAuth authentication for Claude Max subscribers

This release syncs with upstream v0.0.13 and adds OAuth authentication support for Claude Max subscribers.

Update action reference to use commit SHA instead of beta tag