I was a little bit lost here and I think the reason is that the ask is not very clear (and that’s very good because when you figure out the answer you kind feel the try harder/out of box mindset going on)
Long story short, the challenge is not about manipulating the cookie to login back with admin using the application.
Play around with the get request and the cookie and pay attention to server response using burp. The answer is on the server’s response to your request.