chore(scheduler-alpha): minor doc updates (#31939)

### Issue # (if applicable)

Tracking #31785.

### Reason for this change

Updating doc for better clarity.

### Description of changes

Doc updates

### Description of how you validated changes

N/A

### 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*

packages/@aws-cdk/aws-scheduler-alpha/README.md

@@ -85,8 +85,6 @@ const cronBasedSchedule = new Schedule(this, 'Schedule', {
 A one-time schedule is a schedule that invokes a target only once. You configure a one-time schedule when by specifying the time of the day, date, 
 and time zone in which EventBridge Scheduler evaluates the schedule.
 
-[comment]: <> (TODO: Switch to `ts` once Schedule is implemented)
-
 ```ts
 declare const target: targets.LambdaInvoke;
 
@@ -208,11 +206,6 @@ const target = new targets.LambdaInvoke(fn, {
 });
 ```
 
-
-### Cross-account and cross-region targets
-
-Executing cross-account and cross-region targets are not supported yet.
-
 ### Specifying Encryption key
 
 EventBridge Scheduler integrates with AWS Key Management Service (AWS KMS) to encrypt and decrypt your data using an AWS KMS key. 

packages/@aws-cdk/aws-scheduler-alpha/lib/input.ts

@@ -2,17 +2,12 @@ import { DefaultTokenResolver, IResolveContext, Stack, StringConcat, Token, Toke
 import { ISchedule } from './schedule';
 
 /**
- * The text, or well-formed JSON, passed to the target of the schedule.
+ * The text or well-formed JSON input passed to the target of the schedule.
+ * Tokens and ContextAttribute may be used in the input.
  */
 export abstract class ScheduleTargetInput {
   /**
-   * Pass text to the target, it is possible to embed `ContextAttributes`
-   * that will be resolved to actual values while the CloudFormation is
-   * deployed or cdk Tokens that will be resolved when the CloudFormation
-   * templates are generated by CDK.
-   *
-   * The target input value will be a single string that you pass.
-   * For passing complex values like JSON object to a target use method
+   * Pass simple text to the target. For passing complex values like JSON object to a target use method
    * `ScheduleTargetInput.fromObject()` instead.
    *
    * @param text Text to use as the input for the target
@@ -22,8 +17,7 @@ export abstract class ScheduleTargetInput {
   }
 
   /**
-   * Pass a JSON object to the target, it is possible to embed `ContextAttributes` and other
-   * cdk references.
+   * Pass a JSON object to the target. The object will be transformed into a well-formed JSON string in the final template.
    *
    * @param obj object to use to convert to JSON to use as input for the target
    */
@@ -66,7 +60,8 @@ class FieldAwareEventInput extends ScheduleTargetInput {
 }
 
 /**
- * Represents a field in the event pattern
+ * A set of convenient static methods representing the Scheduler Context Attributes.
+ * These Context Attributes keywords can be used inside a ScheduleTargetInput.
  *
  * @see https://docs.aws.amazon.com/scheduler/latest/UserGuide/managing-schedule-context-attributes.html
  */
@@ -103,7 +98,7 @@ export class ContextAttribute {
   }
 
   /**
-   * Escape hatch for other ContextAttribute that might be resolved in future.
+   * Escape hatch for other Context Attributes that may be added in the future
    *
    * @param name - name will replace xxx in <aws.scheduler.xxx>
    */