chore: make backend pass clippy with strict warnings

[ubugeeei]

Finding

backend does not pass cargo clippy --all-targets -- -D warnings. These are mostly mechanical but block using clippy as a production gate.

Evidence

• clippy reports redundant closures, collapsible if statements, type complexity, new_without_default, manual clamp, and unnecessary cast warnings.

Acceptance criteria

• Resolve current clippy warnings in backend.
• cargo clippy --all-targets -- -D warnings passes in backend.
• Keep behavior equivalent.

[ubugeeei]

対応済みです。修正は PR #1 / commit 9cf4498 に反映済みです。