Refactor agent spawning and delegation check mechanisms

- Updated agent spawning from `Task()` to `Agent()` across various files to align with new standards.
- Enhanced the `code-developer` agent description to clarify its invocation context and responsibilities.
- Introduced a new `delegation-check` skill to validate command delegation prompts against agent role definitions, ensuring content separation and conflict detection.
- Established comprehensive separation rules for command delegation prompts and agent definitions, detailing ownership and conflict patterns.
- Improved documentation for command and agent design specifications to reflect the updated spawning patterns and validation processes.

.claude/skills/prompt-generator/specs/command-design-spec.md

@@ -153,15 +153,15 @@ Display banners before major phase transitions (agent spawning, user decisions,
 
 ## Agent Spawning Pattern
 
-Commands spawn agents via `Task()` with structured prompts:
+Commands spawn agents via `Agent()` with structured prompts:
 
-```markdown
-Task(
-  prompt=filled_prompt,
-  subagent_type="agent-name",
-  model="{model}",
-  description="Verb Phase {X}"
-)
+```javascript
+Agent({
+  subagent_type: "agent-name",
+  prompt: filled_prompt,
+  description: "Verb Phase {X}",
+  run_in_background: false
+})
 ```
 
 ### Prompt Structure for Agents