Address PR comments

Author: blkt

docs/toolhive/guides-k8s/deploy-registry.mdx

@@ -53,11 +53,8 @@ flowchart LR
 
 ## Create a registry
 
-You can create `MCPRegistry` resources in namespaces based on how the operator
-was deployed.
-
-- **Cluster mode (default)**: Create MCPRegistry resources in any namespace
-- **Namespace mode**: Create MCPRegistry resources only in allowed namespaces
+You can create `MCPRegistry` resources in the namespaces where the ToolHive
+Operator is deployed.
 
 See [Deploy the operator](./deploy-operator-helm.mdx#operator-deployment-modes)
 to learn about the different deployment modes.
@@ -360,7 +357,10 @@ spec:
 
 When customizing containers in `podTemplateSpec`, you must use
 `name: registry-api` for the main container to ensure the operator can properly
-manage the Registry server.
+manage the Registry server. The container name is hardcoded to avoid conflict
+issues with user provided containers. Mandating a container name on the Operator
+side explicitly tells the Operator it is the main registry server container and
+any other containers provided by the use are sidecars/init containers.
 
 :::
 

docs/toolhive/guides-registry/deployment.mdx

@@ -15,10 +15,9 @@ Although it is possible to run ToolHive Registry to use an in-memory store, it
 is unreliable to run multiple replicas as they would not share state, and you
 should run it with a proper Postgres database.
 
-### Deployment using the Operator
+### ToolHive Operator
 
-The recommended way of deploying the Registry server is by using the ToolHive
-Operator. See
+ToolHive Operator supports deploying the Registry server. See
 [Deploy the Registry server in Kubernetes](../guides-k8s/deploy-registry.mdx)
 for a complete guide.