Turn on Claude task lists by default, with a visible toggle in Claude provider settings

[cookernetes]

What

Claude 5 threads only show a task list if you add CLAUDE_CODE_ENABLE_TODO_TOOLS=1 as a free-text environment variable under Settings → Providers → (Claude instance) → Environment. Without it, Claude Code doesn't expose TaskCreate / TaskUpdate / TaskList in headless mode, so the tasks drawer stays empty, while Codex threads show their plan steps automatically.

I'd like:

1. Task tools on by default for Claude sessions (set CLAUDE_CODE_ENABLE_TODO_TOOLS=1 when the variable is unset).
2. A visible "Show task list" toggle in the Claude provider settings to turn it off. An explicit CLAUDE_CODE_ENABLE_TODO_TOOLS=0 still wins.

Why now

• fix(claude): restore plan updates for Claude 5 sessions #9031 implemented the default (with the explicit-0 opt-out agreed in review) and was closed only because the provider layer was being rewritten for V2, with a note to raise it again once V2 landed. V2 merged in feat(orchestrator): introduce new orchestrator #2829 on 2 Oct.
• fix(web): Claude task lists stay in the composer between turns #18392 made the drawer keep Claude task lists between turns, but noted that it "does not enable task tools", so the display side is ready and only the opt-in is missing.
• [Bug]: Unfinished task list disappears from the composer when the turn ends #14327 calls it out as a gap: "main doesn't set it for Claude 5 sessions yet ([Bug]: Plan sidebar stays empty on Claude 5 models — Claude Code no longer exposes the Task tools by default #9029)".

Today's workaround

Setting the variable (in T3's provider environment, or env in ~/.claude/settings.json) works: the tools appear and the drawer shows Claude's steps. It's hard to find, though: only the Claude provider docs mention it, and an empty drawer gives no hint.

Version: 0.1.2-nightly.20261021.3457 (Claude Code 2.1.306, macOS arm64)