Studio Code: generate the tool list for live WordPress.com site sessions too

[youknowriad]

Related issues

• Fixes STU-2508
• Follows Let wpcom_request work on any WordPress.com site #5003 (STU-2496)

How AI was used in this PR

Written with Claude Code. I reviewed the diff; Claude ran lint, typecheck and the CLI AI tests, and checked the change by rendering the system prompts before and after it.

Proposed Changes

Studio Code's system prompt lists the session's tools from the tools themselves (#4858), but only for local sites. Sessions on a live WordPress.com site still had a hand-written tool list, which drifts whenever a tool changes (#5003 had to edit it by hand).

• Both kinds of session now get their tool list and tool guidelines from the tools they register, so the list can't drift from what the agent can actually call.
• wpcom_request now describes itself in the prompt, like the other tools.
• Live-site sessions also get the file tools' usage guidelines (Write size limits, batching edits), which they were missing.
• The one live-site note the hand-written list carried (create a local site before pulling into it) moved to the live-site rules. That Read/Write/Edit/Ls only touch scratch files was already said there.

The local-site prompt is byte-for-byte unchanged, so local site builds behave as before.

Testing Instructions

• npm test -- apps/cli/ai/tests/system-prompt.test.ts
• In Studio Code on a live WordPress.com site (no eval covers these sessions):
  1. npm run cli:build && node apps/cli/dist/cli/main.mjs code
  2. Pick a WordPress.com site in the site picker.
  3. Ask "What's the title of my latest post?", then make a small change (e.g. "Change the tagline to …").
  4. The agent calls wpcom_request with the site's ID, and both requests work.

Pre-merge Checklist

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

🤖 Generated with Claude Code

[wpmobilebot]

📊 Performance Test Results

Comparing bd3e969 vs trunk

app-size

Metric	trunk	bd3e969	Diff	Change
App Size (Mac)	1456.80 MB	1456.80 MB	0.00 MB	⚪ 0.0%

site-editor

Metric	trunk	bd3e969	Diff	Change
load	1180 ms	1171 ms	9 ms	⚪ 0.0%

site-startup

Metric	trunk	bd3e969	Diff	Change
siteCreation	7062 ms	7056 ms	6 ms	⚪ 0.0%
siteStartup	3387 ms	3368 ms	19 ms	⚪ 0.0%

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Results are median values from multiple test runs.

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