chore: naming-convention-ref-name (14 warnings)

[steilerDev]

Parent tracking issue: #1455

Summary

Resolve all 14 `@eslint-react/naming-convention-ref-name` warnings. The rule enforces a `Ref` suffix on variables holding ref objects.

Fix pattern

```tsx
// before
const input = useRef(null);

// after
const inputRef = useRef(null);
```

Rename the ref and all its references within the component. A quick find-and-replace within the file usually suffices.

Scope

Production code (`client/src/`).

Acceptance Criteria

• `npm run lint` reports 0 `@eslint-react/naming-convention-ref-name` warnings
• All ref consumers updated (no dangling references)
• No behavioral changes

Risk

Very low. Pure rename.