Webpack file cache isn't generated when webacpack watch option is false/nothing

[KiriRea]

• Operating System: Windows 10
• Node Version: 16.15.0
• NPM Version: 8.5.5
• webpack Version: 5.73.0
• karma-webpack Version: 5.0.0

Expected Behavior

It generates webpack file cache regardless of webpack watch option(true/false) when execute karma test.

Actual Behavior

I want to generate webpack file cache when I execute karma test.
https://webpack.js.org/configuration/cache/

When I don't write webpack watch option(or write "false" to watch option) on webpack config, webapack file cache is not generated.
After investigate this problem, I found below issue, and this issue says that call compiler.close() when it generates webpack file cache.
webpack/webpack#15411
->you need to call compiler.close() in callback to store cache.

However "karma-webpack/controller.js" doesn't call compiler.close() when watch option is false/nothing.
Therefore, it looks like this causes webpack can't generate file cache.

• karma-webpack/lib/karma-webpack/controller.js(Line 56-90)
  https://github.com/ryanclark/karma-webpack/blob/master/lib/karma-webpack/controller.js

  setupExitHandler(compiler) {
    this.karmaEmitter.once('exit', (done) => {
      compiler.close(() => {
        console.log('Webpack stopped watching.');
        done();
      });
    });
  }
  
  ...

  _bundle() {
    this.isActive = true;

    return new Promise((resolve) => {
      if (this.webpackOptions.watch === true) {
        console.log('Webpack starts watching...');
        this.compiler = webpack(this.webpackOptions, (err, stats) =>
          this.handleBuildResult(err, stats, resolve)
        );

        this.setupExitHandler(this.compiler);
      } else {
        this.compiler = webpack(this.webpackOptions).run((err, stats) =>
          this.handleBuildResult(err, stats, resolve)
        );
      }
    });
  }

why it doesn't call compiler.close() if watch option is false/nothing?

Code

• script

karma start karma.conf.js

• karma.config.js

var webpackConfig = require('webpack.config');
...
module.exports = {
    ...
    webpack: webpackConfig,
    ...
}

• webpack.config.js

...
module.exports = {
    devtool: 'inline-source-map',
    mode: 'development',
    ...
    watch: false,
    ...
    cache: {
        type: 'filesystem',
        name: 'sample',

        buildDependencies: {
            config: [__filename],
        }
    }
}

How Do We Reproduce?

Write watch option(false) and cache config to webpack.config.js like above code.
Then execute karma(karma start karma.conf.js).