aws-cdk-lib(core): App Inherits From Stage, But Doesn't Allow Setting Region

### Describe the bug

I believe there's a fundamental "miss" in the code for `App`. `App` inherits from `Stage` yet does not allow setting any of the `StageProps`. As defined here https://github.com/aws/aws-cdk/blob/15cb919fab9d20d0e8f0485662131cbb10980269/packages/%40aws-cdk/core/lib/stage.ts#L13-L43, `env` allows setting the region from which all other resources in the stage will use.

Even when casting `as any` to force `env` into `App`s constructor, `App` ignores `props` as a whole and only passes `outdir` as can be seen here: https://github.com/aws/aws-cdk/blob/15cb919fab9d20d0e8f0485662131cbb10980269/packages/%40aws-cdk/core/lib/app.ts#L160-L162

Also of note, not passing a region to a `Stack` constructor's props will default the stack to `us-east-1` even though `--verbose` output shows that `CDK_DEFAULT_REGION` has been correctly pulled from `~/.aws/config`.

### Expected Behavior

I would expect a number of things here:

1. We can set the region for the entire stage, via `App` in `AppProps`
2. The stage and stacks within it would use the value present in `CDK_DEFAULT_REGION` if nothing was specified manually in props
3. There would be a warning that `CDK_DEFAULT_REGION` diverged from what the default value of `us-east-1` with instructions or hints as to how to proceed.

### Current Behavior

The stage silently defaults to `us-east-1`

### Reproduction Steps

Please reference code permalinks above

### Possible Solution

_No response_

### Additional Information/Context

_No response_

### CDK CLI Version

2.68.0

### Framework Version

2.68.0

### Node.js Version

18

### OS

Mac Vetura

### Language

Typescript

### Language Version

4.9

### Other information

_No response_

Start with the linked definitions in packages/@aws-cdk/core/lib/stage.ts and packages/@aws-cdk/core/lib/app.ts, especially StageProps, AppProps, and the App constructor. Check how CDK_DEFAULT_REGION is read and how the current default reaches stacks; done means App can configure the stage region, uses the environment value when appropriate, and gives the requested divergence guidance.

Written by the indexing model from the issue text.