Attach JavaScript and CSS assets when render entity using Web Sockets
It was quite some work to adapt the rendering process. There is a lot of code, I will just summarise the solution. If you want more details, just write a comment.

The solution looks similar to my ideas/hypothesis in the question's description.

I created a custom render which collects all the libraries during rendering in an array. It results in an array:

return [
      'commands' ['An array with ajax commands for settings'],
      'content' =&gt; 'Rendered content(HTML)',
      'libraries' =&gt; 'all the needed assets grouped into libraries',
    ];


I had to to override the AjaxResponseAttachmentsProcessor and AssetResolver classes.

Also I implemented the hook_js_settings_build() to collect all the libraries on the page, as ajaxPageState does not contain all the dependencies.

At the front-end side it is not possible to attach all the assets by comparing ajaxPageState and the response from a Web Socket.