Extensions are not deployed upon creation.

[kurtkanaskie]

When creating an extension you cannot specify "state": "DEPLOYED" as the Edge API returns an error. You must specify "state": "UNDEPLOYED" or omit all together.
You can include credentials on the create.

POST https://api.enterprise.apigee.com/v1/organizations/$ORG/environments/$ENV/extensions
[
   {
      "name":"test-extension",
      "description":"Testing",
      "packageName":"gcp-auth",
      "version":"1.0.2",
      "credentials": "ewogICJ0...udC5jb20iCn0",
      "state": "UNDEPLOYED"
   }
]

To deploy using the plugin you must send a PATCH request with at least the following or the complete create request.

PATCH  https://api.enterprise.apigee.com/v1/organizations/$ORG/environments/$ENV/extensions/$EXT_ID
[
   {
      "name":"test-extension",
      "state": "DEPLOYED"
   }
]

NOTE: that the Edge API does not require the name but the maven plugin does.

Consequently, the plugin does not allow the extension to be undeployed, since the plugin requires a name but the Edge API does not allow the name when setting state to UNDEPLOYED.

The Edge API can deploy using

PATCH  https://api.enterprise.apigee.com/v1/organizations/$ORG/environments/$ENV/extensions/$EXT_ID
{
    "state": "DEPLOYED"
}

The Edge API can undeploy using

PATCH  https://api.enterprise.apigee.com/v1/organizations/$ORG/environments/$ENV/extensions/$EXT_ID
{
    "state": "UNDEPLOYED"
}

Edge API: https://apidocs.apigee.com/extensions-management-api/apis/patch/v1/organizations/%7Borg%7D/environments/%7Benv%7D/extensions/%7Bid%7D-0