Task tools are off by model, with no settings key and no way to keep a session checklist by default

Since 2.1.233, TaskCreate, TaskGet, TaskUpdate, TaskList and TodoWrite are unavailable on Opus 4.8, Sonnet 5, Fable 5 and newer unless CLAUDE_CODE_ENABLE_TODO_TOOLS=1 is set (changelog 2.1.233, tools reference "Task tool availability"). Issue #80487 was closed pointing at that variable.

What we hit, on 2.1.266 with claude-fable-5-1: the tools were absent from the session and from the ToolSearch pool, with nothing in /doctor or the tool list saying why. Our team's process depends on a per-session checklist, and the session fell back to a file in the repository until a docs lookup found the variable.

What we ask:

• A settings.json key for task tools (project level), so a repository can switch them on for every developer without each shell exporting a variable. The env block in project settings did work for us, but nothing in the settings documentation says this variable is honored there.
• When a tool is removed by a model gate, say so in the tool list or /doctor, so a user knows the fix exists.
• Consider task tracking on by default again on the newest models, or document the reasoning for the gate.

Reproduce: run claude with --model claude-fable-5-1 on 2.1.266, ask for the tool list, TaskCreate is missing. Set CLAUDE_CODE_ENABLE_TODO_TOOLS=1 in the project settings env block and it appears.