fix(pid): (updated) verify gateway identity before blocking startup on stale PID

[mrigangha]

📝 Description

The singleton check in WritePidFile only verified that a process with the
recorded PID existed, but did not verify it was actually a picoclaw gateway.
When a gateway crashed without cleaning up its PID file and the OS reused
that PID for an unrelated process (e.g. systemd-resolved), the gateway would
refuse to start and enter a crash loop under systemd.

🗣️ Type of Change

• 🐞 Bug fix (non-breaking change which fixes an issue)
• ✨ New feature (non-breaking change which adds functionality)
• 📖 Documentation update
• ⚡ Code refactoring (no functional changes, no api changes)

🤖 AI Code Generation

• 🤖 Fully AI-generated (100% AI, 0% Human)
• 🛠️ Mostly AI-generated (AI draft, Human verified/modified)
• 👨‍💻 Mostly Human-written (Human lead, AI assisted or none)

🔗 Related Issue

Fixes #2720

📚 Technical Context (Skip for Docs)

• Reference URL:
• Reasoning:

🧪 Test Environment

• Hardware: PC
• OS: Ubuntu 22.04

☑️ Checklist

• My code/docs follow the style of this project.
• I have performed a self-review of my own changes.
• I have updated the documentation accordingly.