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/breakdown-feature-implementation.prompt.md

@@ -1,5 +1,5 @@
 ---
-agent: 'agent'
+mode: 'agent'
 description: 'Prompt for creating detailed feature implementation plans, following Epoch monorepo structure.'
 ---