refactor: move filtering draft posts to backend

[takanome-dev]

What type of PR is this? (check all applicable)

• [ ] 💡 Feature
• [ ] 🐛 Bug Fix
• [ ] 📝 Documentation Update
• [ ] 🎨 Style
• [x] 🧑‍💻 Code Refactor
• [ ] 🔥 Performance Improvements
• [ ] ✅ Test
• [ ] 🤖 Build
• [ ] 🔁 CI
• [ ] ⏩ Revert

Description

This PR moves the logic of filtering draft posts to the server side.

Related Tickets & Documents

Fixes #65

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