Device authorization polling issue / question

[qVipoL]

Hi, im having an question to authenticating a device,
i have this function to poll for a token on the client:

const pollForToken = async (deviceCode: string, initialInterval: number) => {
    let pollingInterval = initialInterval;

    const poll = async () => {
      try {
        const { data, error } = await authClient.device.token({
          grant_type: 'urn:ietf:params:oauth:grant-type:device_code',
          device_code: deviceCode,
          client_id: 'my-app',
        });

        const { data: sessionData } = await authClient.getSession({
          fetchOptions: {
            headers: {
              Authorization: `Bearer ${data?.access_token}`,
            },
          },
        });

        if (error) {
          switch (error.error) {
            case 'authorization_pending':
              // Continue polling
              break;
            case 'slow_down':
              pollingInterval += 5;
              break;
            case 'access_denied':
              setIsPolling(false);
              setUserCode(null);
              toast.error(t('auth.deviceAuthorizationDenied'));
              return;
            case 'expired_token':
              setIsPolling(false);
              setUserCode(null);
              toast.error(t('auth.deviceAuthorizationExpired'));
              return;
            default:
              setIsPolling(false);
              setUserCode(null);
              toast.error(
                error.error_description || t('auth.deviceAuthorizationFailed'),
              );
              return;
          }
        }

        if (!data?.access_token) {
          // Schedule next poll
          pollingTimeoutRef.current = setTimeout(poll, pollingInterval * 1000);
        }
      } catch (err) {
        setIsPolling(false);
        setUserCode(null);
        const errorMessage =
          err instanceof Error
            ? err.message
            : t('auth.deviceAuthorizationNetworkError');
        toast.error(errorMessage);
      }
    };

    // Start polling
    pollingTimeoutRef.current = setTimeout(poll, pollingInterval * 1000);
  };

it works ok until i call authClient.getSession, which sets only "better-auth_session_data" variable in local storage, but as i understand to get authenticated i need "better-auth_cookie" variable to have "better-auth.session_token" set, but i dont understand how it can be generated, which function / endpoint do i need to call after getting the access token?

thanks in advance