I'm using google-cloud-firestore python library in GKE But by default firestore lib is not authorize itself as like it automatically authorize in App Engine you don't need to provide any service-account.json file.
My GKE cluster and firestore native mode is in same project according to my think it should auto authorize on GKE as well but this is not correct.
I know I can authorize firestore library using service-account.json file. But I want to know is I'm doing something wrong or it does not auto authorize in GKE ?
Indeed, you will need the service-account.json for Firestore to authorize the use with GKE, otherwise, it won't be possible to use it. I would recommend you take a look at this below article provides you more information and ideas on how to use GKE with Firestore.
Let me know if the information helped you!