The API is called Cloud Run Admin API.
Cloud Run Admin API
There is an SDK for .NET.
Cloud Run Admin API Client Library for .NET
Namespace Google.Apis.CloudRun.v1
Creating a Cloud Run service is fairly complicated. I recommend that you study the REST API first so that you understand the request body. The .NET library models the REST API.
Method: namespaces.services.create
The key item is the service resource:
Resource: Service
There is a quick way to learn the API request body. Create a simple Cloud Run example and then add the command line option --log-http. Save the output to a file and then study the HTTP request parameters and request body to decipher the very large data structures that are required to create a service.
gcloud run deploy --log-http
I wrote two articles on the Cloud Run Admin API:
- Google Cloud Run Deep Dive – Understanding the APIs – Part 1
- Google Cloud Run Deep Dive – Understanding the APIs – Part 2
Note: I wrote those articles two years ago. Cloud Run has advanced a lot since then. However, these articles will help you understand the low-level details of the service that were not published elsewhere at the time.