Is the following experiment about cookie correct?

can the following experiment summarize the principle in a few short sentences? At present, all I know is that the facts are as follows

.
:Tomcat

:localhost:8080/project
Servlet:localhost:8080/project/MyCookie

localhost:8080/project/MyCookieServlet:

public class MyCookie extends HttpServlet {
    @Override
    protected void doGet(HttpServletRequest request, HttpServletResponse response) throws ServletException, IOException {
        response.setContentType("text/html;charset=utf-8");

        Cookie[] cookies = request.getCookies();
        for(int i = 0; cookies != null && i < cookies.length;iPP){
            //,cookie
            response.getWriter().println("cookie  cookies[i].getName():"+cookies[i].getName()+cookies[i].getValue());
        }
    }
}

:

1.,TomcatCookie,
    :
 Set-Cookie:JSESSIONID=544F9C73731E416ECC15CF5A204C2023; Path=/project; HttpOnly;

2.,Tomcat
    Cookie,,cookie,:
      Cookie:JSESSIONID=544F9C73731E416ECC15CF5A204C2023

3Cookie;

4.Servletlocalhost:8080/project/MyCookie ,
,Servlet,Cookie

5),(4)Servlet,
Servletcookie

Does

4 mean to get the sessionid and then delete it and then access it without getting the sessionid?

tomcat should judge that if there is a sessionid in the request, continue the session. If not, new a new session to return sessionid.
if the cookie containing sessionid is deleted in the browser, the server should think that it is a new session that returns the new sessionid and the path has nothing to do with it

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