ESLINT: errors/warnings are not displayed on console

[psaintjust]

Describe the bug

When running vite-plugin-checker with eslint, the diagnostics results are not displayed. Only the summary is displayed: "[ESLint] Found 12 errors and 3 warnings".
The diagnostics are displayed on the overlay.

This is a regression introduced by: #474

Reproduction

Set up vite-plugin-checker with eslint with basic configuration

Expected behavior

Vite-plugin-checker displays the diagnostics results and the summary result for eslint.

Actual:
Vite-plugin-checker only displays the summary result.

System Info

System:
    OS: macOS 15.3.1
    CPU: (12) x64 Intel(R) Core(TM) i7-9750H CPU @ 2.60GHz
    Memory: 389.84 MB / 16.00 GB
    Shell: 5.9 - /bin/zsh
  Binaries:
    Node: 20.16.0 - /usr/local/bin/node
    Yarn: 1.22.22 - /usr/local/bin/yarn
    npm: 10.9.1 - /usr/local/bin/npm
  Browsers:
    Chrome: 135.0.7049.115
    Safari: 18.3
  npmPackages:
    vite-plugin-checker: ^0.9.1 => 0.9.1

Additional context

No response

Validations

• Read the docs.
• Check that there isn't already an issue that reports the same bug to avoid creating a duplicate.

[psaintjust]

#501