Successfully did the upgrade using the CLI from 14.4 to 15.3.8526 and the solution builds and the frontend site loads up fine. The user can login, however the new dashboard page and the pages list and such are not loading (any URL path containing /adminapp). The CMS displays a green loading icon that never goes away.
There are no errors in the Sitefinity logs, the dev tools console has no errors and all the network requests are 200s. The user can get to some backend areas, such as Settings, Modules and Services, Users and Web Services.

Having tried reinstalling the Telerik.Sitefinity.All package, copying from the packages folder content itself, installing a blank v15 site on the same version and copying the whole folder over, but none of these made a difference. Also tried deleting the entire AdminApp folder and replacing it with empty project solution's (15.3) but it does not make any difference.

The Sitefinity project has been upgraded from version 14.4 to 15.3 using the CLI tool and the site overrode the HTML sanitizer. Here are the following steps to reproduce:

1. In Sitefinity project extends the HTML sanitizer as described in the following documentation link:
https://www.progress.com/documentation/sitefinity-cms/html-sanitization
https://www.progress.com/documentation/sitefinity-cms/html-sanitization#modify-the-html-sanitizer-configuration

2.  For example add the following HtmlSanitizer.cs class in the project:

using System;
using System.Text.RegularExpressions;
using Telerik.Sitefinity.Security.Sanitizers;

namespace SitefinityWebApp
{
  public class SitefinityExtendedHtmlSanitizer : IHtmlSanitizer
  {
    private ExtendedHtmlSanitizer sanitizer = new ExtendedHtmlSanitizer();
    // General HTML sanitization
    public string Sanitize(string html)
    {
      return sanitizer.Sanitize(html);
    }

    public string SanitizeUrl(string url) => sanitizer.SanitizeUrl(url);

    private class ExtendedHtmlSanitizer : HtmlSanitizer
    {
      public ExtendedHtmlSanitizer()
      {
       ...
      }
    }
  }
}

3. Build the project. Restart the Application.

4. Sign-on to Sitefinity backend. Noticed that any access to the URL with /adminapp path (such as Pages, Contents) will hang (3 green dots loading icon will never disappear). However any access to other Administration modules such as Settings, Modules and Services, Users and Web Services are working fine.  

The provided code sample is not based on the Sitefinity documentation. It is not supposed to be implemented from the IHtmlSanitizer interface. Instead it should extend the HtmlSanitizer class. 

The correct custom sanitizer class should looks as follows:

public class SitefinityExtendedHtmlSanitizer : HtmlSanitizer
{
   public SitefinityExtendedHtmlSanitizer() : base()
   {
      ...
   }
}

References to Other Documentation:
https://www.progress.com/documentation/sitefinity-cms/html-sanitization