Agentic UI: Remove unused starred flag from AI chat sessions

[bcotrim]

Related issues

• Fixes STU-2061

How AI was used in this PR

Claude traced every reference to the starred session flag across the codebase, removed the dead plumbing, updated the tests, and ran lint/typecheck/tests. Changes were reviewed and the archive flow was manually tested

Proposed Changes

The star/unstar UI for chat conversations was removed in #4191, which left the starred session-metadata flag as dead plumbing: nothing could set it and nothing displayed it. This PR retires the flag end-to-end — from the shared-config schema, session types and hydration, the IPC handler, the hosted/local PATCH endpoints, and the UI data layer.

• No user-visible behavior changes: starring was already unreachable.
• The archive flow is untouched and keeps working as before.
• No config migration needed: the shared-config schema is loose, so existing shared.json files with leftover starred entries still parse fine. Those stale flags are now purged on the next session-metadata write.

Testing Instructions

• Search the codebase for starred — the only remaining reference is the legacy-flag purge in pruneSharedSessionMetadata (and its test).
• In the agentic UI, open a chat for a site, archive it from the Chat history menu, and confirm it moves to the "Archived chats" dialog.
• Check ~/.studio/shared.json: the archived chat has { "archived": true }, and any pre-existing "starred" entries are removed after that write.

Pre-merge Checklist

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

🤖 Generated with Claude Code

[wpmobilebot]

📊 Performance Test Results

Comparing 48d8a9a vs trunk

app-size

Metric	trunk	48d8a9a	Diff	Change
App Size (Mac)	1352.96 MB	1352.96 MB	+0.00 MB	⚪ 0.0%

site-editor

Metric	trunk	48d8a9a	Diff	Change
load	1085 ms	1072 ms	13 ms	⚪ 0.0%

site-startup

Metric	trunk	48d8a9a	Diff	Change
siteCreation	7003 ms	7003 ms	0 ms	⚪ 0.0%
siteStartup	2360 ms	2361 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)