Remove Claude Code auth provider from AI command

[youknowriad]

Related issues

• Related to ongoing AI command simplification

How AI was used in this PR

Claude Code authored the changes. All modifications were reviewed and verified with typecheck and tests.

Proposed Changes

• Remove the anthropic-claude provider definition, the hasClaudeCodeAuth() function, and the child_process import from apps/cli/ai/providers.ts
• Remove anthropic-claude from the config schema enum in apps/cli/lib/cli-config/core.ts
• Remove Claude-auth-specific tests and the child_process mock from apps/cli/ai/tests/auth.test.ts

Testing Instructions

• Run npm run typecheck — passes cleanly
• Run npm test -- apps/cli/ai/tests/auth.test.ts — all 11 tests pass
• Start the AI command and verify /provider only shows WordPress.com and Anthropic · API key

Pre-merge Checklist

• Have you checked for TypeScript, React or other console errors?

[wpmobilebot]

📊 Performance Test Results

Comparing 3fa1e7c vs trunk

app-size

Metric	trunk	3fa1e7c	Diff	Change
App Size (Mac)	1271.72 MB	1271.72 MB	0.00 MB	⚪ 0.0%

site-editor

Metric	trunk	3fa1e7c	Diff	Change
load	1859 ms	1904 ms	+45 ms	⚪ 0.0%

site-startup

Metric	trunk	3fa1e7c	Diff	Change
siteCreation	8172 ms	8203 ms	+31 ms	⚪ 0.0%
siteStartup	4828 ms	4874 ms	+46 ms	⚪ 0.0%

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Results are median values from multiple test runs.

Legend: 🟢 Improvement (faster) | 🔴 Regression (slower) | ⚪ No change (<50ms diff)