#32249 [Bug]: The token path in cookie is not aligned with SERVER_ROOT_PATH.
### Check for existing issues
- [x] I have searched the existing issues and checked that my issue is not a duplicate.
### What happened?
A bug happened!
<img width="1524" height="519" alt="Image" src="https://github.com/user-attachments/assets/b27a40eb-7805-41b6-859c-d09ba86b5bc3" />
### Steps to Reproduce
1. deploy without SERVER_ROOT_PATH under a.com 2. deploy with SERVER_ROOT_PATH under a.com/SERVER_ROOT_PATH 3. login into a.com and a.com/SERVER_ROOT_PATH in one browser, failed and redirect to /sso/key/generate
### Relevant log output
```shell
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### What part of LiteLLM is this about?
_No response_
### What LiteLLM version are you on ?
v1.81.14
### Twitter / LinkedIn details
_No response_