Feature Request: Support for GitHub Actions schedule trigger

## Feature Request

I'd like to use Claude Code Action with GitHub Actions `schedule` triggers to enable periodic automated tasks.

## Use Case
For example, I'm thinking of using it for weekly maintenance tasks like this:

```yaml
on:
schedule:
- cron: '0 2 * * 1' # Weekly maintenance

jobs:
maintenance:
steps:
- uses: anthropics/claude-code-action@main
with:
direct_prompt: "Analyze the repository for outdated documentation and create pull requests with necessary updates"
```

This would enable:
- Automated documentation maintenance
- Periodic code quality checks
- Regular dependency reviews

## Current Behavior

Schedule triggers are not currently supported. The action fails with:

Error: Unsupported event type: schedule

## Expected Behavior

It would be great if the action could work with schedule triggers. Since schedule events don't have associated PR/issue context, perhaps using direct_prompt with a configurable output target might work well.