Use ha-dialog for dialog-area-registry-detail

[joshmcrty]

Proposed change

This replaces the use of ha-paper-dialog with ha-dialog for the Area settings dialog on the Area registry detail page. It also adds a public closeDialog method per #6138

Type of change

• Dependency upgrade
• Bugfix (non-breaking change which fixes an issue)
• New feature (thank you!)
• Breaking change (fix/feature causing existing functionality to break)
• Code quality improvements to existing code or addition of tests

Example configuration

Create a new area on the Areas page, or click on an area on the Areas page, then click on the gear icon in the top right corner to open the new dialog.

Additional information

• This PR fixes or closes issue: fixes #
• This PR is related to issue: Move all paper-dialogs to ha-dialogs #6138
• Link to documentation pull request:

Checklist

• The code change is tested and works locally.
• There is no commented out code in this PR.
• Tests have been added to verify that the new code works.

If user exposed functionality or configuration variables are added/changed:

• Documentation added/updated for www.home-assistant.io