The new jwt would not be returned from the identity provider as a cookie. That would not make much sense as the client on a different origin would not be able to read it. Instead, the token is passed in the response body, or even the url (usually not the token in that case, but let's not delve into that).
So the idp has its httpOnly cookie to authenticate the user, issues a new token in some way that is not a cookie, and the client stores the token for the appropriate origin (not the idp) in say localstorage. This way, any call to the resource server is not vulnerable to csrf, because the token needs to be explicitly be added from localstorage. The idp can be called by attacker.com to issue a new token ("csrf"), but attacker.com will not have access to the token due to the same origin policy, so it's not exploitable.
Note that even if the new token is returned as a cookie for the idp and read from there by the client, it's still ok, because the idp will do nothing with that token, and the resource server (~api) will not receive it automatically.
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