fix(prompts): change agent: to mode: in frontmatter

Fixed 22 prompt files:
- Changed 'agent:' to 'mode:' (correct frontmatter key)
- Removed duplicate 'search' entries from tools arrays

This aligns with prompt authoring rules in prompt.instructions.md

.github/prompts/structured-autonomy-implement.prompt.md

@@ -2,7 +2,7 @@
 name: sa-implement
 description: 'Structured Autonomy Implementation Prompt'
 model: GPT-5 mini (copilot)
-agent: agent
+mode: agent
 ---
 
 You are an implementation agent responsible for carrying out the implementation plan without deviating from it.