fix(rds): clusterScailabilityType is spelled wrong and should be clusterScalabilityType (#32825)

### Issue #32415 

Closes #32415 .

### Reason for this change

Misspelling of the `ClusterScalabilityType` type, enum, and prop.

### Description of changes

Deprecated misspellings of **ClusterScailabilityType**/**clusterScailabilityType** and aliased the misspelling for backwards compatibility. The misspelled name will be removed in the next MV release.

### Describe any new or updated permissions being added

No permissions changes.

### Description of how you validated changes

Added unit tests for the new spelling (ClusterScalabilityType/clusterScalabilityType), and kept unit tests that tested the misspelling.
```zsh
# in packages/aws-cdk-lib
yarn test aws-rds
```
<img width="822" alt="Screenshot 2025-01-09 at 16 10 04" src="https://github.com/user-attachments/assets/9626a0c1-0a5f-45fb-a052-1b1697a5fbdd" />

Ran the relevant integration test.
```zsh
# in packages/@aws-cdk-testing/framework-integ
yarn integ test/aws-rds/test/integ.cluster-limitless.js
```
<img width="916" alt="Screenshot 2025-01-09 at 17 03 44" src="https://github.com/user-attachments/assets/0ed33a38-f6d8-44ee-a210-81e37af5439f" />

Ran Rosetta to verify README changes.
```zsh
./scripts/run-rosetta.sh
```
No complications from README changes in these commits.



### Checklist
- [x] My code adheres to the [CONTRIBUTING GUIDE](https://github.com/aws/aws-cdk/blob/main/CONTRIBUTING.md) and [DESIGN GUIDELINES](https://github.com/aws/aws-cdk/blob/main/docs/DESIGN_GUIDELINES.md)

----

*By submitting this pull request, I confirm that my contribution is made under the terms of the Apache-2.0 license*

Author: iankhou

packages/aws-cdk-lib/aws-rds/README.md

@@ -1436,7 +1436,7 @@ new rds.DatabaseCluster(this, 'LimitlessDatabaseCluster', {
     version: rds.AuroraPostgresEngineVersion.VER_16_4_LIMITLESS,
   }),
   vpc,
-  clusterScailabilityType: rds.ClusterScailabilityType.LIMITLESS,
+  clusterScalabilityType: rds.ClusterScalabilityType.LIMITLESS,
   // Requires enabling Performance Insights
   enablePerformanceInsights: true,
   performanceInsightRetention: rds.PerformanceInsightRetention.MONTHS_1,

packages/aws-cdk-lib/aws-rds/lib/cluster.ts

@@ -450,7 +450,17 @@ interface DatabaseClusterBaseProps {
    *
    * Set LIMITLESS if you want to use a limitless database; otherwise, set it to STANDARD.
    *
+   * @default ClusterScalabilityType.STANDARD
+   */
+  readonly clusterScalabilityType?: ClusterScalabilityType;
+
+  /**
+   * [Misspelled] Specifies the scalability mode of the Aurora DB cluster.
+   *
+   * Set LIMITLESS if you want to use a limitless database; otherwise, set it to STANDARD.
+   *
    * @default ClusterScailabilityType.STANDARD
+   * @deprecated Use clusterScalabilityType instead. This will be removed in the next major version.
    */
   readonly clusterScailabilityType?: ClusterScailabilityType;
 }
@@ -492,6 +502,25 @@ export enum InstanceUpdateBehaviour {
 /**
  * The scalability mode of the Aurora DB cluster.
  */
+export enum ClusterScalabilityType {
+  /**
+   * The cluster uses normal DB instance creation.
+   */
+  STANDARD = 'standard',
+
+  /**
+   * The cluster operates as an Aurora Limitless Database,
+   * allowing you to create a DB shard group for horizontal scaling (sharding) capabilities.
+   *
+   * @see https://docs.aws.amazon.com/AmazonRDS/latest/AuroraUserGuide/limitless.html
+   */
+  LIMITLESS = 'limitless',
+}
+
+/**
+ * The scalability mode of the Aurora DB cluster.
+ * @deprecated Use ClusterScalabilityType instead. This will be removed in the next major version.
+ */
 export enum ClusterScailabilityType {
   /**
    * The cluster uses normal DB instance creation.
@@ -701,6 +730,10 @@ abstract class DatabaseClusterNew extends DatabaseClusterBase {
   constructor(scope: Construct, id: string, props: DatabaseClusterBaseProps) {
     super(scope, id);
 
+    if (props.clusterScalabilityType !== undefined && props.clusterScailabilityType !== undefined) {
+      throw new Error('You cannot specify both clusterScalabilityType and clusterScailabilityType (deprecated). Use clusterScalabilityType.');
+    }
+
     if ((props.vpc && props.instanceProps?.vpc) || (!props.vpc && !props.instanceProps?.vpc)) {
       throw new Error('Provide either vpc or instanceProps.vpc, but not both');
     }
@@ -802,7 +835,7 @@ abstract class DatabaseClusterNew extends DatabaseClusterBase {
       throw new Error('`enablePerformanceInsights` disabled, but `performanceInsightRetention` or `performanceInsightEncryptionKey` was set');
     }
 
-    if (props.clusterScailabilityType === ClusterScailabilityType.LIMITLESS) {
+    if (props.clusterScalabilityType === ClusterScalabilityType.LIMITLESS || props.clusterScailabilityType === ClusterScailabilityType.LIMITLESS) {
       if (!props.enablePerformanceInsights) {
         throw new Error('Performance Insights must be enabled for Aurora Limitless Database.');
       }
@@ -877,7 +910,7 @@ abstract class DatabaseClusterNew extends DatabaseClusterBase {
       }),
       storageType: props.storageType?.toString(),
       enableLocalWriteForwarding: props.enableLocalWriteForwarding,
-      clusterScalabilityType: props.clusterScailabilityType,
+      clusterScalabilityType: props.clusterScalabilityType ?? props.clusterScailabilityType,
       // Admin
       backtrackWindow: props.backtrackWindow?.toSeconds(),
       backupRetentionPeriod: props.backup?.retention?.toDays(),
@@ -1287,7 +1320,7 @@ export class DatabaseCluster extends DatabaseClusterNew {
     setLogRetention(this, props);
 
     // create the instances for only standard aurora clusters
-    if (props.clusterScailabilityType !== ClusterScailabilityType.LIMITLESS) {
+    if (props.clusterScalabilityType !== ClusterScalabilityType.LIMITLESS && props.clusterScailabilityType !== ClusterScailabilityType.LIMITLESS) {
       if ((props.writer || props.readers) && (props.instances || props.instanceProps)) {
         throw new Error('Cannot provide writer or readers if instances or instanceProps are provided');
       }

packages/aws-cdk-lib/aws-rds/test/cluster.test.ts

@@ -17,12 +17,34 @@ import {
   DatabaseClusterEngine, DatabaseClusterFromSnapshot, ParameterGroup, PerformanceInsightRetention, SubnetGroup, DatabaseSecret,
   DatabaseInstanceEngine, SqlServerEngineVersion, SnapshotCredentials, InstanceUpdateBehaviour, NetworkType, ClusterInstance, CaCertificate,
   IClusterEngine,
+  ClusterScalabilityType,
   ClusterScailabilityType,
   DBClusterStorageType,
 } from '../lib';
 
 describe('cluster new api', () => {
   describe('errors are thrown', () => {
+    test('when both clusterScalabilityType and clusterScailabilityType (deprecated) props are provided', () => {
+      // GIVEN
+      const stack = testStack();
+      const vpc = new ec2.Vpc(stack, 'VPC');
+
+      expect(() => {
+        // WHEN
+        new DatabaseCluster(stack, 'Database', {
+          engine: DatabaseClusterEngine.AURORA_MYSQL,
+          instanceProps: {
+            instanceType: ec2.InstanceType.of(ec2.InstanceClass.BURSTABLE2, ec2.InstanceSize.SMALL),
+            vpc,
+          },
+          clusterScalabilityType: ClusterScalabilityType.STANDARD,
+          clusterScailabilityType: ClusterScailabilityType.STANDARD,
+          iamAuthentication: true,
+        });
+        // THEN
+      }).toThrow('You cannot specify both clusterScalabilityType and clusterScailabilityType (deprecated). Use clusterScalabilityType.');
+    });
+
     test('when old and new props are provided', () => {
       // GIVEN
       const stack = testStack();
@@ -165,7 +187,10 @@ describe('cluster new api', () => {
       });
     });
 
-    test('cluster scalability option', () => {
+    test.each([
+      ['clusterScalabilityType', 'clusterScalabilityType', ClusterScalabilityType.STANDARD],
+      ['clusterScailabilityType (deprecated)', 'clusterScailabilityType', ClusterScailabilityType.STANDARD],
+    ])('cluster scalability option with %s', (_, propName, propValue) => {
       // GIVEN
       const stack = testStack();
       const vpc = new ec2.Vpc(stack, 'VPC');
@@ -174,8 +199,8 @@ describe('cluster new api', () => {
       new DatabaseCluster(stack, 'Cluster', {
         engine: DatabaseClusterEngine.AURORA_MYSQL,
         vpc,
-        clusterScailabilityType: ClusterScailabilityType.STANDARD,
         writer: ClusterInstance.serverlessV2('writer'),
+        [propName]: propValue,
       });
 
       // THEN
@@ -186,7 +211,10 @@ describe('cluster new api', () => {
     });
 
     describe('limitless database', () => {
-      test('with default options', () => {
+      test.each([
+        ['clusterScalabilityType', 'clusterScalabilityType', ClusterScalabilityType.LIMITLESS],
+        ['clusterScailabilityType (deprecated)', 'clusterScailabilityType', ClusterScailabilityType.LIMITLESS],
+      ])('with default options using %s', (_, propName, propValue) => {
         // GIVEN
         const stack = testStack();
         const vpc = new ec2.Vpc(stack, 'VPC');
@@ -197,7 +225,7 @@ describe('cluster new api', () => {
             version: AuroraPostgresEngineVersion.VER_16_4_LIMITLESS,
           }),
           vpc,
-          clusterScailabilityType: ClusterScailabilityType.LIMITLESS,
+          [propName]: propValue,
           enablePerformanceInsights: true,
           performanceInsightRetention: PerformanceInsightRetention.MONTHS_1,
           monitoringInterval: cdk.Duration.minutes(1),