It embeds a Google Chrome browser control in a Delphi form.
TWebBrowser is an embedded Internet Explorer control. It might have access to cookies and other data from your Internet Explorer settings, but it won't have access to any other browsers' settings, including Firefox and Chrome.
The embedded Chrome browser will not have access to the user's Chrome or Firefox settings. Those are entirely separate applications, and your application doesn't get any special standing related to them just because it's using an embedded browser control. If you want to gain access to another application's settings, you'll have to do it the same way anyone else does.