[containerservice] Migrate containerservice projects to use snippets extraction (Azure#32695)

### Packages impacted by this PR

- @azure/arm-containerservice
- @azure/arm-containerservicefleet
- @azure-rest/arm-containerservice

### Issues associated with this PR

- Azure#32416

### Describe the problem that is addressed by this PR

Updates all projects under `astro` to use snippets extraction.

### What are the possible designs available to address the problem? If
there are more than one possible design, why was the one in this PR
chosen?


### Are there test cases added in this PR? _(If not, why?)_


### Provide a list of related PRs _(if any)_


### Command used to generate this PR:**_(Applicable only to SDK release
request PRs)_

### Checklists
- [ ] Added impacted package name to the issue description
- [ ] Does this PR needs any fixes in the SDK Generator?** _(If so,
create an Issue in the
[Autorest/typescript](https://github.com/Azure/autorest.typescript)
repository and link it here)_
- [ ] Added a changelog (if necessary)

Author: mpodwysocki

common/config/rush/pnpm-lock.yaml

@@ -50,29 +50,29 @@ The following section shows you how to initialize and authenticate your client,
 
 ### List All Managed Clusters
 
-```typescript
-import ContainerServiceManagementClient, { paginate } from "@azure-rest/arm-containerservice";
+```ts snippet:SampleReadmeListManagedClusters
 import { DefaultAzureCredential } from "@azure/identity";
+import ContainerServiceClient, { isUnexpected, paginate } from "@azure-rest/arm-containerservice";
 
-async function listManagedClusters() {
-  const subscriptionId = process.env.SUBSCRIPTION_ID as string;
-  const credential = new DefaultAzureCredential();
-  const client = ContainerServiceManagementClient(credential);
-  const initialResponse = await client
-    .path(
-      "/subscriptions/{subscriptionId}/providers/Microsoft.ContainerService/managedClusters",
-      subscriptionId,
-    )
-    .get();
-  const result = paginate(client, initialResponse);
-  const resArray = new Array();
-  for await (let item of result) {
-    resArray.push(item);
-  }
-  console.log(resArray);
+const subscriptionId = "00000000-0000-0000-0000-000000000000";
+const credential = new DefaultAzureCredential();
+const client = ContainerServiceClient(credential);
+
+const initialResponse = await client
+  .path(
+    "/subscriptions/{subscriptionId}/providers/Microsoft.ContainerService/managedClusters",
+    subscriptionId,
+  )
+  .get();
+
+if (isUnexpected(initialResponse)) {
+  throw initialResponse;
 }
 
-listManagedClusters().catch(console.error);
+const result = paginate(client, initialResponse);
+for await (const item of result) {
+  console.log(`Managed Cluster: ${item.name}`);
+}
 ```
 
 ## Troubleshooting
@@ -81,7 +81,7 @@ listManagedClusters().catch(console.error);
 
 Enabling logging may help uncover useful information about failures. In order to see a log of HTTP requests and responses, set the `AZURE_LOG_LEVEL` environment variable to `info`. Alternatively, logging can be enabled at runtime by calling `setLogLevel` in the `@azure/logger`:
 
-```javascript
+```ts snippet:SetLogLevel
 import { setLogLevel } from "@azure/logger";
 
 setLogLevel("info");

sdk/containerservice/arm-containerservice-rest/README.md

@@ -24,9 +24,7 @@
   "files": [
     "dist/",
     "README.md",
-    "LICENSE",
-    "review/*",
-    "CHANGELOG.md"
+    "LICENSE"
   ],
   "//metadata": {
     "constantPaths": [
@@ -64,33 +62,33 @@
     "unit-test": "npm run unit-test:node && npm run unit-test:browser",
     "unit-test:browser": "npm run clean && dev-tool run build-package && dev-tool run build-test && dev-tool run test:vitest --browser",
     "unit-test:node": "dev-tool run test:vitest",
-    "update-snippets": "echo skipped"
+    "update-snippets": "dev-tool run update-snippets"
   },
   "sideEffects": false,
   "autoPublish": false,
   "dependencies": {
     "@azure-rest/core-client": "^1.0.0",
     "@azure/abort-controller": "^2.1.2",
-    "@azure/core-auth": "^1.3.0",
+    "@azure/core-auth": "^1.9.0",
     "@azure/core-lro": "^3.1.0",
-    "@azure/core-rest-pipeline": "^1.8.0",
-    "@azure/logger": "^1.0.0",
-    "tslib": "^2.2.0"
+    "@azure/core-rest-pipeline": "^1.18.2",
+    "@azure/logger": "^1.1.4",
+    "tslib": "^2.8.1"
   },
   "devDependencies": {
     "@azure-tools/test-credential": "^2.0.0",
     "@azure-tools/test-recorder": "^4.1.0",
     "@azure-tools/test-utils-vitest": "^1.0.0",
     "@azure/dev-tool": "^1.0.0",
     "@azure/eslint-plugin-azure-sdk": "^3.0.0",
-    "@azure/identity": "^4.0.1",
+    "@azure/identity": "^4.6.0",
     "@types/node": "^18.0.0",
     "@vitest/browser": "^3.0.3",
     "@vitest/coverage-istanbul": "^3.0.3",
     "autorest": "latest",
     "dotenv": "^16.0.0",
     "eslint": "^9.9.0",
-    "playwright": "^1.49.1",
+    "playwright": "^1.50.0",
     "typescript": "~5.7.2",
     "vitest": "^3.0.3"
   },