core: Stage name check allows underscores ('_') and periods ('.') while stack name does not allow them

### Describe the bug

The following code

```ts
pipeline.addStage(new AppStage(this, "Stage per acme.example.com"));
```

results into the following `synth` error

```bash
Error: invalid stage name "Stage per acme.example.com". Stage name must start with a letter and contain only alphanumeric characters, hypens ('-'), underscores ('_') and periods ('.')
```

According to error message I can use underscores and periods. My next try with the code

```ts
pipeline.addStage(new AppStage(this, "Stage_per_acme.example.com"));
```

results into the following `synth` error

```bash
Error: Stack name must match the regular expression: /^[A-Za-z][A-Za-z0-9-]*$/, got 'Stage_per_acme.example.com-HelloCdkStack'
```

### Expected Behavior

Provide clear error message what characters are allowed for stage id.

### Current Behavior

Error message reads that underscores and periods are allowed for stage id but `synth` returns errors for those.

### Reproduction Steps

See https://github.com/yuyokk/aws-cdk-stage-name-bug/blob/main/lib/hello-cdk-stack.ts

```ts
// lib/hello-cdk-stack.ts

import { Stack, StackProps, Stage, StageProps } from "aws-cdk-lib";
import {
CodePipeline,
CodePipelineSource,
ShellStep,
} from "aws-cdk-lib/pipelines";
import { Construct } from "constructs";

export class PipelineStack extends Stack {
constructor(scope: Construct, id: string, props?: StackProps) {
super(scope, id, props);

const pipeline = new CodePipeline(this, "Pipeline", {
crossAccountKeys: true,
synth: new ShellStep("Synth", {
input: CodePipelineSource.gitHub("yuyokk/tenant-core", "main"),
commands: ["npm ci", "npm run build", "npx cdk synth"],
}),
});

pipeline.addStage(new AppStage(this, "Stage per acme.example.com"));
// pipeline.addStage(new AppStage(this, "Stage_per_acme.example.com"));
}
}

class AppStage extends Stage {
constructor(scope: Construct, id: string, props?: StageProps) {
super(scope, id, props);

new HelloCdkStack(this, "HelloCdkStack");
}
}

class HelloCdkStack extends Stack {
constructor(scope: Construct, id: string, props?: StackProps) {
super(scope, id, props);
}
}
```

```ts
// bin/hello-cdk.ts

#!/usr/bin/env node
import "source-map-support/register";
import * as cdk from "aws-cdk-lib";
import { PipelineStack } from "../lib/hello-cdk-stack";

const app = new cdk.App();
new PipelineStack(app, "HelloCdkStack");
```

### Possible Solution

Fix stage name check to be consistent with stack id checks.

PR for a possible fix https://github.com/aws/aws-cdk/pull/23089

### Additional Information/Context

_No response_

### CDK CLI Version

2.51.1

### Framework Version

_No response_

### Node.js Version

v16.18.1

### OS

macOS 13.0.1

### Language

Typescript

### Language Version

_No response_

### Other information

_No response_

The reproduction is in lib/hello-cdk-stack.ts, with the application entry point in bin/hello-cdk.ts; start by running the shown npm and npx cdk synth commands to reproduce the validation mismatch. Review PR #23089 before making changes, and consider the issue complete when stage-name guidance and synth behavior are consistent.

Written by the indexing model from the issue text.