docs: update the list of available APIs (#4621)

Author: yoshi-code-bot

README.md

@@ -164,6 +164,7 @@ applications that interact with individual Google Cloud services:
 | [Private Catalog](https://github.com/googleapis/google-cloud-node/tree/main/packages/google-cloud-privatecatalog) | [![Preview][preview-stability]][launch-stages] | [![npm](https://img.shields.io/npm/v/@google-cloud/private-catalog)](https://npm.im/@google-cloud/private-catalog) |
 | [Public Certificate Authority](https://github.com/googleapis/google-cloud-node/tree/main/packages/google-cloud-security-publicca) | [![Preview][preview-stability]][launch-stages] | [![npm](https://img.shields.io/npm/v/@google-cloud/publicca)](https://npm.im/@google-cloud/publicca) |
 | [Rapid Migration Assessment API](https://github.com/googleapis/google-cloud-node/tree/main/packages/google-cloud-rapidmigrationassessment) | [![Preview][preview-stability]][launch-stages] | [![npm](https://img.shields.io/npm/v/@google-cloud/rapidmigrationassessment)](https://npm.im/@google-cloud/rapidmigrationassessment) |
+| [SQL Admin API](https://github.com/googleapis/google-cloud-node/tree/main/packages/google-cloud-sql) | [![Preview][preview-stability]][launch-stages] | [![npm](https://img.shields.io/npm/v/@google-cloud/sql)](https://npm.im/@google-cloud/sql) |
 | [Storage Insights API](https://github.com/googleapis/google-cloud-node/tree/main/packages/google-cloud-storageinsights) | [![Preview][preview-stability]][launch-stages] | [![npm](https://img.shields.io/npm/v/@google-cloud/storageinsights)](https://npm.im/@google-cloud/storageinsights) |
 | [Support API](https://github.com/googleapis/google-cloud-node/tree/main/packages/google-cloud-support) | [![Preview][preview-stability]][launch-stages] | [![npm](https://img.shields.io/npm/v/@google-cloud/support)](https://npm.im/@google-cloud/support) |
 | [Trace](https://github.com/googleapis/cloud-trace-nodejs) | [![Preview][preview-stability]][launch-stages] | [![npm](https://img.shields.io/npm/v/@google-cloud/trace-agent)](https://npm.im/@google-cloud/trace-agent) |

libraries.json

@@ -2810,6 +2810,23 @@
     "linkToRepoHomepage": "https://github.com/googleapis/google-cloud-node/tree/main/packages/google-cloud-rapidmigrationassessment",
     "support_documentation": "https://cloud.google.com/migration-center/docs/getting-support"
   },
+  {
+    "name": "sql",
+    "name_pretty": "SQL Admin API",
+    "product_documentation": "",
+    "client_documentation": "https://cloud.google.com/nodejs/docs/reference/sql/latest",
+    "issue_tracker": "https://github.com/googleapis/google-cloud-node/issues",
+    "release_level": "preview",
+    "language": "nodejs",
+    "repo": "googleapis/google-cloud-node",
+    "distribution_name": "@google-cloud/sql",
+    "api_id": "sqladmin.googleapis.com",
+    "default_version": "v1",
+    "requires_billing": true,
+    "library_type": "GAPIC_AUTO",
+    "api_shortname": "sql",
+    "linkToRepoHomepage": "https://github.com/googleapis/google-cloud-node/tree/main/packages/google-cloud-sql"
+  },
   {
     "name": "storageinsights",
     "name_pretty": "Storage Insights API",