aws-backup: BackupPlanName is not unique, when generated (unlike the rest of the properties that are handled either by CDK or CFn)

### Describe the bug

Greetings and salutations!

Source for bug: https://github.com/aws/aws-cdk/blob/8a62b589f662ead0d354ee519a04186f7f207193/packages/aws-cdk-lib/aws-backup/lib/plan.ts#L177

Unlike any other auto-gen props, this one copies the `id` when not supplied, causing collisions (a resource already using the name and therefore others not being created because of it).

### Regression Issue

- [ ] Select this option if this issue appears to be a regression.

### Last Known Working CDK Library Version

_No response_

### Expected Behavior

The generated name should be unique and in line with the service regEx.

### Current Behavior

Synth works when having two stacks in the same app, both having the same backupPlan `id`, but fails when deploying.

### Reproduction Steps

1. Define a stack that declares the backup plan
2. Skip the `backupPlanName` in the props provided to the constructor
3. Declare two instances of the same Stack type in the same App/ Account
4. Observe deployment failing

### Possible Solution

Use the logic available in https://github.com/aws/aws-cdk/blob/main/packages/aws-cdk-lib/core/lib/private/unique-resource-name.ts

### Additional Information/Context

_No response_

### AWS CDK Library version (aws-cdk-lib)

2.257.0

### AWS CDK CLI version

2.1125.0

### Node.js Version

22.23.1

### OS

all

### Language

TypeScript

### Language Version

_No response_

### Other information

_No response_

Start in packages/aws-cdk-lib/aws-backup/lib/plan.ts at the BackupPlanName generation referenced in the report, then compare it with packages/aws-cdk-lib/core/lib/private/unique-resource-name.ts. Reproduce the two-stacks case with backupPlanName omitted and verify that synthesized names are unique and valid for the AWS Backup service regex.

Written by the indexing model from the issue text.