Errors when using with the webpack dev server 4

Issue description

I got errors when using bundle analyzer wit the webpack dev server 4.

Error parsing bundle asset "d:\projects\devel\rankrocket\app\www\js\app.a49e5464.js": no such file
Error parsing bundle asset "d:\projects\devel\rankrocket\app\www\js\pdfmake.d2d0b128.js": no such file
Error parsing bundle asset "d:\projects\devel\rankrocket\app\www\js\vendors.aa8b04ed.js": no such file
Error parsing bundle asset "d:\projects\devel\rankrocket\app\www\js\private.18a4a042.js": no such file
Error parsing bundle asset "d:\projects\devel\rankrocket\app\www\js\public.6ce47ae2.js": no such file
Error parsing bundle asset "d:\projects\devel\rankrocket\app\www\js\node_modules_fortawesome_fontawesome-free_css_all_min_css.2124fe27.js": no such file
Webpack Bundle Analyzer is started at http://127.0.0.1:8888

This happens only, when running under dev server, regular build completes normally.

Technical info

System:
    OS: Windows 10 10.0.19043
    CPU: (8) x64 Intel(R) Core(TM) i7-10510U CPU @ 1.80GHz
    Memory: 5.88 GB / 15.78 GB
  Binaries:
    Node: 16.10.0 - d:\devel\node\node.exe
    npm: 7.20.2 - ~\.npm\npm.cmd

webpack: 5.55.1
webpack-dev-server: 4.3.0
webpack-bundle-analyzer: 4.4.2

Debug info

I am using it as plugin with the following options:

new BundleAnalyzerPlugin( {
        "analyzerMode": process.env.WEBPACK_DEV_SERVER ? "server" : "static",
        "analyzerPort": 8888,
        "openAnalyzer": false,
})

What other Webpack plugins were used?

html-webpack-plugin
copy-webpack-plugin
terser-webpack-plugin
case-sensitive-paths-webpack-plugin
mini-css-extract-plugin
css-minimizer-webpack-plugin

Reproduce the report with webpack 5.55.1, webpack-dev-server 4.3.0, and webpack-bundle-analyzer 4.4.2 using the shown plugin options. Start by tracing how the analyzer resolves assets under dev server mode; done when those assets are parsed without errors while regular static builds continue to work.