I have a .Net core web Api calling google drive api. The google drive api should authenticate the api call with Okta and authorize. How can this be achieved?
The domain of the api will be google.api.com ... so no where it is going to Okta for authentication
What you do with your Okta site will be after you have gained access to the google api on behalf of your users. a bearer token from Okta will not grant you access to a google api you need to go though googles authorization server to get that.
In order to access the Google Drive api and access private user data. The owner of that data will need to authorize your access.
To do this we use something called Oauth2. The issue you will have is begin that you say you are using a web api to call Google you will need to create a web application on the side where your users can authorize your application to access their data. You will need to register your application with google on Google Developer console. Create a web client credentials. Then when the user has authorized your application to access their data you will will need to store the refresh token in your system associated with the user.
Then your web api will be able to access the users data by loading the refresh token and requesting a new access token.
There is currently only one sample web-applications-asp.net-core-3 for .net core web applications it doesn't show how to store the refresh token you will need to work that out.
I do have a video on setting up asp .net core with the google people api it might give you a starting point How to get a Google users profile information, with C#. as well as one on how to create a How to create Google Oauth2 web application credentials in 2021.