Validate Anthropic API key in api-key and provider commands in Studio Code CLI

[sejas]

Related issues

• Closes STU-2245

How AI was used in this PR

AI helped identify and build the code.

Proposed Changes

This PR validates the key at entry time, in both /api-key and /provider (both funnel through the provider's prepare step), and displays an error if the key is not valid.
It only affects CLI. The UI is being implemented in #4503

Testing Instructions

1. npm run cli:build && node apps/cli/dist/cli/main.mjs code
2. Run /api-key and enter a made-up key (e.g. fake key): the prompt shows "Anthropic rejected this API key. Check the key and try again." and stays open. Enter a real key: it saves.
3. Edit ~/.studio/cli.json and corrupt the saved anthropicApiKey, then run /provider and pick "Anthropic · API key": the CLI re-prompts for a key instead of accepting the broken one.
4. Offline check: disconnect the network and run /api-key with any non-empty key — it saves (unverifiable ≠ invalid).

validate-api-key-when-saving-cli.mp4

Pre-merge Checklist

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

[bcotrim]

Changes LGTM 👍

Changing provider doesn't clear the saved key, so we can still boot straight into a dead one — isReady() is just Boolean(anthropicApiKey) (providers.ts:211) and the auto-fallback never calls prepare. Worth validating at boot too, or is the startup round trip too costly? Fine as a follow-up either way.

[bcotrim]

I've pushed an empty commit to trigger the full CI checks (E2E, Performance tests)

[wpmobilebot]

📊 Performance Test Results

Comparing 8de6983 vs trunk

app-size

Metric	trunk	8de6983	Diff	Change
App Size (Mac)	1406.51 MB	1406.29 MB	0.21 MB	⚪ 0.0%

site-editor

Metric	trunk	8de6983	Diff	Change
load	1070 ms	1044 ms	26 ms	⚪ 0.0%

site-startup

Metric	trunk	8de6983	Diff	Change
siteCreation	7538 ms	7550 ms	+12 ms	⚪ 0.0%
siteStartup	2866 ms	2865 ms	1 ms	⚪ 0.0%

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Results are median values from multiple test runs.

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