docs: update Aspire operator docs (#1149)

- Adjusted Markdown syntax for note and tip blocks.

Author: kimpenhaus

README.md

@@ -102,49 +102,6 @@ aspire run --project src/MyApp.AppHost/MyApp.AppHost.csproj
 aspire publish --project src/MyApp.AppHost/MyApp.AppHost.csproj --output-path ./artifacts/k8s
 ```
 
-Common AppHost shapes:
-
-Local development only:
-
-```csharp
-var dev = builder.AddKubernetesEnvironment("dev");
-
-builder.AddKubeOps<Projects.AspireOperator>("operator")
-    .RunWithKubernetes(dev, run => run.WithPersistentCrds());
-```
-
-Azure publish/deploy only:
-
-```csharp
-var aks = builder.AddAzureKubernetesEnvironment("aks");
-
-builder.AddKubeOps<Projects.AspireOperator>("operator")
-    .PublishAsKubernetesOperator(aks, publish => publish.WithServiceAccount("operator"));
-```
-
-Local run and Azure deploy:
-
-```csharp
-var dev = builder.AddKubernetesEnvironment("dev");
-var aks = builder.AddAzureKubernetesEnvironment("aks");
-
-builder.AddKubeOps<Projects.AspireOperator>("operator")
-    .RunWithKubernetes(dev)
-    .PublishAsKubernetesOperator(aks);
-```
-
-Publish only without an Aspire Kubernetes environment:
-
-```csharp
-builder.AddKubeOps<Projects.AspireOperator>("operator")
-    .PublishAsKubernetesOperator(publish =>
-    {
-        publish.Namespace = "operator-system";
-        publish.WithServiceAccount("operator");
-    });
-```
-
-Without `RunWithKubernetes(...)`, `AddKubeOps<TProject>(...)` keeps the operator in explicit-start mode for local Aspire runs. Standalone manifest publish does not require `AddKubernetesEnvironment(...)`, Helm, or a live cluster; publishing with a Kubernetes environment generates an Aspire Helm chart, while `aspire deploy` installs that chart into the selected environment.
 
 ## Packages
 
@@ -201,4 +158,4 @@ In short:
 
 ## Motivation
 
-KubeOps aims to provide a first-class experience for developing Kubernetes operators within the .NET ecosystem, offering an alternative to Go-based SDKs like Kubebuilder and Operator SDK, while embracing familiar C# patterns and tooling.
+KubeOps aims to provide a first-class experience for developing Kubernetes operators within the .NET ecosystem, offering an alternative to Go-based SDKs like Kubebuilder and Operator SDK, while embracing familiar C# patterns and tooling.

docs/docs/operator/aspire.mdx

@@ -54,7 +54,7 @@ await host.RunAsync();
 - **HTTP resilience** — the standard resilience handler (retries, circuit breaker, timeouts) is applied to all `HttpClient` instances.
 - **Health checks** — a default `self` liveness check tagged `live`.
 
-:::tip Operator name
+:::tip[Operator name]
 The OpenTelemetry service name and the tracing source name must match `OperatorSettings.Name` — otherwise the operator's reconciliation traces are never captured. Call `AddKubeOpsServiceDefaults()` **after** `AddKubernetesOperator()` so KubeOps can resolve the configured name automatically. If you must call it earlier, pass the name explicitly (and keep it in sync with `OperatorSettings.Name`):
 
 ```csharp
@@ -96,7 +96,7 @@ builder.Build().Run();
 - `RunWithKubernetes(k8s)` opts the operator into local execution against a Kubernetes target.
 - `PublishAsKubernetesOperator(k8s)` includes the operator, CRDs, RBAC, and service account in the Aspire Kubernetes publish/deploy output.
 
-:::note Project reference
+:::note[Project reference]
 When referencing `KubeOps.Aspire.Hosting` from an AppHost, mark it as a normal code reference so the AppHost SDK does not treat it as a resource:
 
 ```xml
@@ -233,4 +233,4 @@ builder.AddKubeOps<Projects.AspireOperator>("operator")
     .PublishAsKubernetesOperator(aks, publish => publish.WithServiceAccount("operator"));
 ```
 
-For the deeper run/publish model, see [Aspire Kubernetes Operator Model](./aspire-kubernetes-model).
+For the deeper run/publish model, see [Aspire Kubernetes Operator Model](./aspire-kubernetes-model).