Todo extension: prompt-induced overhead, and whether it should stay a default

**What problem would this solve?**

The todo extension's prompts pressure models into checklist bookkeeping that raises cost without improving outcomes.

I benchmarked todo on/off as a single-variable A/B (Terminal-Bench 2.1, 26 tasks, k=3, stock goose) across four models:

| model | pass rate (off → on) | cost delta (on) |
|---|---|---|
| haiku-4.5 | 62.8% → 71.8% | +18% |
| sonnet-5 | 78.2% → 80.8% (noise) | +17% |
| opus-5 | 88.5% → 88.5% | +45% (median; means are outlier-dominated) |
| gpt-5.6-sol | 79.5% → 85.9% | +49% |

Three findings point at the prompts, not the tool:

1. The overhead is induced turns and per-turn context, not the tool calls or schema, so lazy-loading the tool would not recover it.
2. On hard tasks (FrontierBench, 10 tasks), todo improved nothing but sonnet-5 spent +39% on end-of-task "closure loops": re-verifying finished work to check off remaining items. The instructions say `End: verify all complete`.
3. Usage is near-universal (85-100% of trials) but uncorrelated with success. The empty-list turn reminder ("Once given a task, immediately update your todo with all explicit and implicit requirements") causes usage.

I then tested two variants on the models that benefit from todo:

| variant | gpt-5.6-sol | haiku-4.5 |
|---|---|---|
| stock todo on (baseline) | 85.9% at $0.165/trial | 65.4% at $0.188 |
| stock todo off (baseline) | 79.5% at $0.110 | 61.5% at $0.154 |
| V1: tool kept, prompts reframed as optional planning notes | 84.6% at $0.089 | 65.4% at $0.151 |
| V2: tool removed, one system-prompt line: brief plan first | 83.3% at $0.115 | 70.5% at $0.155 |

Both variants keep the pass-rate benefit at or below todo-off cost. Under V1, models nearly stop calling the tool while keeping the benefit. The instructions, not the tool, are the active ingredient. (k=3: treat pass-rate deltas as directional, the cost effects are consistent across all arms.)

**What would a good outcome look like?**

Two decisions, in increasing scope:

1. **Prompt fix (small, data-backed):** the todo instructions and turn reminder stop demanding completion and verification, and stop nagging when the list is empty. Tested language is available.
2. **Default status:** decide whether todo should remain a default extension. With pressure-free prompts the tool is rarely called, and a single planning line matches its measured benefit. Its remaining value is the interactive progress UX and a compaction-surviving scratchpad - weigh that against the extension surface (tool schema, per-turn context injection).

**Possible approaches**

- **Path A:** replace the instruction, tool-description, and turn-reminder strings in `crates/goose/src/agents/platform_extensions/todo.rs`. No behavior change otherwise.
- **Path B:** make todo opt-in and add the planning line to the system prompt. Needs desktop UX input, since the checklist is user-visible there.
- Path A stands alone and is worth doing even if Path B is rejected; if Path B proceeds, it supersedes A.

- [x] I have verified this does not duplicate an existing feature request