I've asked Firebase Support about the API Limits and got the following response:
The API’s quota applies depending on the Firebase API you want to
use. In this case the API quota applies to the use of the Firebase Auth REST API. Using it, you can query the Firebase Auth backend
through a REST API. Also, it can be used for various operations such
as creating new users, signing in existing ones and editing or
deleting these users.
To create, and refresh a token the quota will apply, if you use the
REST API to do the operations. However, even if you don’t use the REST
API there are other internal quotas associated with the refreshing of
the token. In order to avoid refreshing the token so many times, set
forceRefresh to false to minimize unneeded token refreshes when a
valid token may still be cached.
I've also asked about the internal quota when refreshing the token using the official sdk and got this reponse:
Unfortunately, some quotas are internal, and confidential information.
For this reason, I am not able to share it with you. However, if you
receive quota errors you can contact us
The rate limit includes both the Client and Admin SDK:
The API limits encapsulates every request that comes from the API.
This includes various operations such as creating new users, signing
in existing ones, and editing or deleting users. The limits apply to
requests coming from both the Client and Admin SDK. This means that
Firebase allows you to have 1000 simultaneous requests/second (both
from Client and Admin SDK) in a project.
~ Firebase Support