Method: cases.patch

 case="projects/some-project/cases/43595344"
curl \
  --request PATCH \
  --header "Authorization: Bearer $(gcloud auth print-access-token)" \
  --header "Content-Type: application/json" \
  --data '{
    "priority": "P1"
  }' \
  "https://cloudsupport.googleapis.com/v2/$case?updateMask=priority" 

 import googleapiclient.discovery

apiVersion = "v2"
supportApiService = googleapiclient.discovery.build(
    serviceName="cloudsupport",
    version=apiVersion,
    discoveryServiceUrl=f"https://cloudsupport.googleapis.com/$discovery/rest?version={apiVersion}",
)
request = supportApiService.cases().patch(
    name="projects/some-project/cases/43112854",
    body={
        "displayName": "This is Now a New Title",
        "priority": "P2",
    },
)
print(request.execute())