[Bug]: Plan sidebar stays empty on Claude 5 models — Claude Code no longer exposes the Task tools by default

Before submitting

• I searched existing issues and did not find a duplicate.
• I included enough detail to reproduce or investigate the problem.

Area

apps/server

Steps to reproduce

1. Start a new thread on the Claude provider with a Claude 5 family model (Fable 5, Sonnet 5, Opus 5; bundled Claude Code 2.1.252).
2. Ask for multi-step work and request progress tracking with tasks.
3. Watch the plan sidebar.

Expected behavior

Task updates stream into the plan sidebar, as they did after #1541 and as Codex plan steps do.

Actual behavior

The sidebar never populates. The session's init event lists no TaskCreate/TaskUpdate/TaskList tools, so the server's mapping to turn.plan.updated has nothing to consume.

Per Anthropic's docs (https://code.claude.com/docs/en/agent-sdk/todo-tracking#model-availability), Agent SDK 0.3.233+ leaves the task-tracking tools out of sessions on Opus 4.8, Sonnet 5, Fable 5, and Mythos 5 unless the embedding application opts in. TodoWrite is gone in the same versions, so both branches of the #1541 mapping are dead for Claude 5 sessions. Haiku 4.5 sessions still get the tools, confirming the model gate. The docs direct applications that render these tool calls to set CLAUDE_CODE_ENABLE_TODO_TOOLS=1.

Suggested fix

Set CLAUDE_CODE_ENABLE_TODO_TOOLS=1 in the Claude session environment (makeClaudeEnvironment). Verified locally against the bundled binary: with the variable set (via env or a Claude settings.json env map), a Fable 5 session exposes TaskCreate/TaskGet/TaskList/TaskUpdate and the sidebar populates again through the existing mapping, with no client changes.

Start in apps/server and locate makeClaudeEnvironment, then inspect how Claude session environment variables are assembled. Set CLAUDE_CODE_ENABLE_TODO_TOOLS=1 and reproduce a Claude 5 session with multi-step work. Done means Task tools appear in the init event and updates populate the existing plan sidebar without client changes.