Yes, I am using the 5 setting plus below setting in my application
<cfset THIS.name="testapplication">
<cfset This.loginstorage="Session">
<cfset THIS.clientManagement=True>
<cfset THIS.sessionManagement=True>
<cfset THIS.setClientCookies=true>
<cfset THIS.sessioncookie.secure = true>
<cfset THIS.sessioncookie.httponly = true>
<cfset THIS.applicationTimeout=createtimespan(0,2,30,0)>
<cfset THIS.sessionTimeout=createtimespan(0,0,30,0)>
<cfset THIS.sessioncookie.httponly=true>
Do you realize that in using THIS.sessioncookie.secure=true, that means that if you're accessing your pages with http rather than https, it will indeed seem not to maintain your session--as it tells the browser that cf's session cookie should only be sent back if the request uses https. And since you're also using this.loginstorage="Session", that's why your cflogin processing would also not work as expected.
But again, none of this is a change in behavior between cf2016 and other recent versions before or since. (You've not said what version you were on before this "new server". Was the old also running cf2016? If not, what version?)