I tried Request.RawUrl and Request.Url (and its properties in the Immediate window).
None did show the extra attribute the setting (web.config):
<sesionState cookieless="true" />
makes in the url.
Example
http://localhost:2677/WebSite1/(S(3abhbgwjg33aqrt3uat2kh4d))/cookielesssessiondetection.aspx
However if you're after that part, 3abhbgwjg33aqrt3uat2kh4d
, you can get it via:
Session.SessionID
Update after the updated question:
I put in my test application a Hyperlink control on the page. In code behind, Page_Load, I added:
HyperLink1.NavigateUrl = Response.ApplyAppPathModifier("About.aspx");
When I run that page then the url to About.aspx gets set with the cookieless session part included.
When I check the source of the rendered html in my browser I see this:
<a id="HyperLink1" href="/WebSite1/(S(3tzgdnmhwxmxqer10d11auuq))/About.aspx">HyperLink</a>