[FEATURE] Support SessionStart hooks in Cowork (Claude Desktop App)

Preflight Checklist

• [x] I have searched existing requests and this feature hasn't been requested yet
• [x] This is a single feature request (not multiple features)

Problem Statement

Cowork sessions do not fire SessionStart hooks defined in ~/.claude/settings.json or in plugins. There is no reliable way to run automated setup actions at the start of a Cowork session.
The only workaround is putting instructions in CLAUDE.md, but Claude routinely skips these in favor of responding to the user's first message. This forces users to send a throwaway "boot up" message before their real question just to trigger initialization — every single session.

Proposed Solution

SessionStart hooks from ~/.claude/settings.json and installed plugins should fire at the start of every Cowork session, the same way they do in Claude Code CLI. The hook's stdout should be injected into context before Claude processes the user's first message.

Alternative Solutions

• CLAUDE.md with "BLOCKING" instructions — unreliable, Claude skips them when the user's first message is engaging
• Scheduled tasks — no "on session start" trigger, only cron/one-time/manual
• Telling users to send "boot up" as their first message every session — works but bad UX

Priority

High - Significant impact on productivity

Feature Category

Configuration and settings

Use Case Example

1. User has a persistent memory system in Google Drive (Obsidian vault with config, active projects, and session logs)
2. At session start, they need to mount Google Drive via request_cowork_directory and run a session-autoload skill
3. In Claude Code CLI, this works perfectly as a SessionStart hook
4. In Cowork, there is no equivalent — the user must manually prompt Claude to do this every session, and if they forget, Claude operates without any prior context

Additional Context

Related issue: #27398 (plugin hooks not firing in Cowork on Windows). This request is broader — SessionStart hooks from both user settings and plugins should work in Cowork across all platforms.