refactor: Remove hardcoded Web Research section from system prompt

- Web Research instructions now come from skills/research/SKILL.md
- Skills are dynamically loaded and injected via generate_skills_prompt()
- Remove test_both_prompts_have_web_research test (no longer applicable)
- Remove unused G3Status::research_complete() function

This completes the externalization of research as a skill.

prompts/system/native.md

@@ -158,27 +158,6 @@ facts:
 3. After all work is complete, write `envelope.yaml` with facts about the completed work
 4. **THEN** call `plan_write` to mark the final item done - verification will check both files
 
-# Web Research
-
-When you need to look up documentation, search for resources, find data online, or research a topic to complete your task, use the **research skill**. Research runs in the background while you continue working.
-
-**Use the research skill** for any web research tasks:
-- Researching APIs, SDKs, libraries, frameworks, or tools
-- Finding approaches, patterns, or best practices
-- Investigating bugs, issues, or error messages
-- Looking up documentation or specifications
-
-**How to use the research skill:**
-1. Start research with `background_process`: `background_process("research-topic", ".g3/bin/g3-research 'your query'")`
-2. Continue with other work while research runs in the background (30-120 seconds)
-3. Check status: `shell(".g3/bin/g3-research --list")` or `shell(".g3/bin/g3-research --status <id>")`
-4. Read the report when ready: `read_file(".g3/research/<id>/report.md")`
-
-**Key points:**
-- Always use `background_process`, never blocking `shell` for research
-- Reports are saved to disk, not auto-injected - read them when you need them
-- Check `.g3/research/<id>/status.json` for machine-readable status
-
 # Workspace Memory
 
 Workspace memory is automatically loaded at startup alongside AGENTS.md. It contains an index of features -> code locations, patterns, and entry points as well as important patterns and invariants.