refactor: rename "Rooms" integration to "Custom Areas"

[DefinitelyADev]

Rename the entire "Rooms" integration to "Custom Areas" to better reflect its functionality and usage. The renaming affects:

• directory and file names: custom_components/rooms -> custom_components/areas
• documentation, comments, and strings references to the "Rooms" entity
• README and other markdown files to clarify the new scope
• update entity IDs and names to use "area_" prefixes

This change aligns the integration's name with its features of managing custom area sensors in Home Assistant, providing clarity to users and developers.

[Copilot]

Pull Request Overview

This PR renames the entire "Rooms" integration to "Custom Areas Integration" to better align with its functionality of managing custom area sensors in Home Assistant.

• Renames domain from "rooms" to "areas" with corresponding directory structure changes
• Updates all entity IDs and prefixes from "room_" to "custom_area_" or "area_"
• Renames classes and configuration keys throughout the codebase

Reviewed Changes

Copilot reviewed 22 out of 24 changed files in this pull request and generated 1 comment.

Show a summary per file

File	Description
validate.py	Updates validation script to check for areas directory and domain
run_tests.py	Updates test runner to target areas test directory
run_mypy.sh	Updates mypy script to check areas directory
pyrightconfig.json	Updates include path to areas directory
hacs.json	Changes integration name to "Custom Areas Integration"
docs/*.md	Updates documentation references from Rooms to Custom Areas
custom_components/areas/translations/en.json	Updates user-facing strings from "Room" to "Area"
custom_components/areas/tests/*.py	Updates test files with new class names and imports
custom_components/areas/strings.json	Updates configuration strings to use "Area" terminology
custom_components/areas/sensor.py	Renames classes and updates entity ID prefixes
custom_components/areas/manifest.json	Updates domain and integration name
custom_components/areas/const.py	Changes domain and configuration constants
custom_components/areas/config_flow.py	Renames config flow class and updates field names
custom_components/areas/init.py	Updates setup functions and logging messages
check_all.py	Updates validation script to check areas directory
README.md	Comprehensive updates from Rooms to Custom Areas terminology
.github/workflows/*.yml	Updates CI/CD workflows to target areas directory

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