[Enhancement] Separate Error Logs into a Dedicated File in log-manager

## Description
Currently, our `log-manager` component receives and processes a large volume of log inputs. To better manage and monitor log information, we propose to categorize logs by directing error logs (ERROR level) to a specific `error.log` file, while other log levels continue to be output to the `server.log` file.

## User Stories
- As a **developer**, I want to easily distinguish and filter error logs to quickly locate issues.
- As a **system administrator**, I need a clear logging policy for routine system monitoring and maintenance.

## Expected Features
1. The `log-manager` should be able to direct logs to different files based on log levels.
2. Error logs (ERROR level) should be directed to `error.log`.
3. All other log levels (such as INFO, WARN, DEBUG, etc.) should be directed to `server.log`.

Start by locating the log-manager component and its existing file-output configuration, then inspect how log levels are routed. Done means ERROR records appear in error.log, while INFO, WARN, DEBUG, and other non-ERROR records continue in server.log, with coverage for both destinations.

Written by the indexing model from the issue text.