Add User-Agent headers to Continue Proxy and CLI requests

[sestinj]

Summary by cubic

Adds User-Agent headers to Continue Proxy and CLI requests to improve observability and meet provider requirements. Extension requests include IDE info; CLI requests include the CLI version.

• New Features
  • Continue Proxy now sends Continue/<extensionVersion> (<ideName>; <ideType>) on all requests.
  • CLI adds Continue-CLI/<version> to request headers for continue-proxy and other providers.

^{Written for commit d5d1f0a. Summary will update automatically on new commits.}

[github-actions]

⚠️ PR Title Format

Your PR title doesn't follow the conventional commit format, but this won't block your PR from being merged. We recommend using this format for better project organization.

Expected Format:

<type>[optional scope]: <description>

Examples:

• feat: add changelog generation support
• fix: resolve login redirect issue
• docs: update README with new instructions
• chore: update dependencies

Valid Types:

feat, fix, docs, style, refactor, perf, test, build, ci, chore, revert

This helps with:

• 📝 Automatic changelog generation
• 🚀 Automated semantic versioning
• 📊 Better project history tracking

This is a non-blocking warning - your PR can still be merged without fixing this.

[github-actions]

✅ Review Complete

Code Review Summary

⚠️ Continue API authentication failed. Please check your CONTINUE_API_KEY.

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[cubic-dev-ai]

No issues found across 2 files

[cubic-dev-ai]

No issues found across 1 file