refactor(be): improve client user & notice module error handling logic

[Lee-won-hyeok]

Description

Client User 및 Notice 모듈에서의 예외 처리 로직을 개선합니다.

Additional context

---

Before submitting the PR, please make sure you do the following

• [ ] Read the Contributing Guidelines
• [ ] Read the Contributing Guidelines and follow the Commit Convention
• [ ] Provide a description in this PR that addresses what the PR is solving, or reference the issue that it solves (e.g. fixes #123).
• [ ] Ideally, include relevant tests that fail without this PR but pass with it.