[Dependency] `esolver → io` same-layer call

[Critsium-xy]

Describe the Code Quality Issue

• Symptom: esolver heavily calls io's writers (output_log, cif_io, print_info, module_ctrl/*, etc.; 37 sites).

Additional Context

• Note: this is the intended call direction (esolver drives output). Once io is split into input/output, esolver → io-output holds naturally and is compliant. No dedicated cleanup needed — just place io-output above/beside esolver in the final layering so it can be called.

Task list for Issue attackers (only for developers)

• Identify the specific code file or section with the code quality issue.
• Investigate the issue and determine the root cause.
• Research best practices and potential solutions for the identified issue.
• Refactor the code to improve code quality, following the suggested solution.
• Ensure the refactored code adheres to the project's coding standards.
• Test the refactored code to ensure it functions as expected.
• Update any relevant documentation, if necessary.
• Submit a pull request with the refactored code and a description of the changes made.