Session not kept after /token and /auth openid to another tab

Hi,
I can’t stay logged to keycloak after doing:
the request for the /openid-connect/token and then with this access_token, I use /openid-connect/auth .
It’s returning 200 and give me the cookie AUTH_SESSION_ID / AUTH_SESSION_ID_LEGACY .
It miss the KEYCLOAK_IDENTITY, KEYCLOAK_SESSION cookies.

My goal is to keep my user authenticated if a user is logged, if he switch tab.
Right now, it goes back to my login page.
It does work if I impersonate from Keycloak and open multiple tabs.

Any way to get this cookies with a request?

Thanks in advance