Seeing two session cookies
Both are failing with

Interesting. Maybe try erasing your local application cache from devtools which will log you out, and then try logging back in?
I just tried this and I'm still seeing the same single session token on my end. It's possible that OpenAI is actively testing new things, so let me know if you keep experiencing this.
I signed in using a different google account and got a single session token. Odd!
Can confirm there is a dual token system in place, wasn't clear to me what causes this but one of my accounts is a paying openapi account:

this is a problem for accounts that have been authorized via google
I'm using a google-authorized account and am only seeing a single session token. So it has to be either something else or a combination of factors.
I also encounter this issue quite often. Both tokens are valid though so you can just select the first one if multiple are detected https://github.com/acheong08/ChatGPT/blob/7be51f67fd1087d1c4d0672f40b225d8c57bdf2f/src/revChatGPT/revChatGPT.py#L363-L378