Setting output to false still outputs stuff

[romulof]

Describe what happened

When i set output: false it will outputs lots of data to stdout/stderr.

Steps to reproduce the issue:

1. Configure Webpack plugin like this:

new BuildPlugin({
  datadog: {
    apiKey: 'xxx',
    prefix: 'yyy',
    tags: ['zzz'],
    output: false,
  },
}),

2. Run the build
3. Get lots of stuff in your terminal

Expected behaviour:

Do not output to stdout/stderr

Actual behaviour:

Lots of stuff is outputted to stdout/stderr

Additional context

macOS 14.3.1 Node.js 18.18.0