Enter brainstorming at the current research need

[nzy1997]

Brainstorming currently restarts a fixed conversation even when the user has already chosen a direction or asked for a concrete derivation. This PR routes by the current need: open exploration keeps Socratic guidance and optional advisor discovery, while a selected problem, resumed session, or requested report enters at that point. Advisor execution and append-only session history move to task-specific references.

The design follows OpenAI's Rethinking skills and prompts for GPT-6 Astra, while preserving the shared Claude/Codex interaction defaults validated during #62. It is the brainstorming slice split from #62 after review feedback.

Validation

• python3 scripts/validate_skills.py: 16 skills pass
• targeted brainstorming/resource tests: 47 passed
• python3 -m pytest -q: 269 passed, 5 skipped
• the independent-install test follows the moved advisor and history references
• git diff --check: clean

[GiggleLiu]

Closing. This rewrite drops the parts that define brainstorm-ideas: the six conversation principles, the mentor tone, the Phase 0–3 structure, the session picker, and the wrap-up rituals (reflection, final recommendation, "you think, I fetch"). It also inverts principle (b) and edits existing tests to fit. Entering at the current need is a fair goal, but it belongs as a short routing paragraph on top of the existing skill, not a replacement of it.