Extract entity template functions into an entity Jinja2 extension

[frenck]

Proposed change

This PR is part of the ongoing effort to refactor our huge single template monolith into something more maintainable. In previous PRs I've moved many categories of template methods out of the monolith template file into their own Jinja2 extension.

This PR moves the entity template functions (entity_name, is_hidden_entity) into their own Jinja2 extension. Moves all tests as well.

There is no functional change in this PR, it is only moving these methods and tests into an extension.

Type of change

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

Additional information

• This PR fixes or closes issue: fixes #
• This PR is related to issue:
• Link to documentation pull request:
• Link to developer documentation pull request:
• Link to frontend pull request:

Checklist

• I understand the code I am submitting and can explain how it works.
• The code change is tested and works locally.
• Local tests pass. Your PR cannot be merged unless tests pass
• There is no commented out code in this PR.
• I have followed the development checklist
• I have followed the perfect PR recommendations
• The code has been formatted using Ruff (ruff format homeassistant tests)
• Tests have been added to verify that the new code works.
• Any generated code has been carefully reviewed for correctness and compliance with project standards.

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

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

If the code communicates with devices, web services, or third-party tools:

• The manifest file has all fields filled out correctly.
  Updated and included derived files by running: python3 -m script.hassfest.
• New or updated dependencies have been added to requirements_all.txt.
  Updated by running python3 -m script.gen_requirements_all.
• For the updated dependencies a diff between library versions and ideally a link to the changelog/release notes is added to the PR description.

To help with the load of incoming pull requests:

• I have reviewed two other open pull requests in this repository.

[Copilot]

Pull request overview

This pull request continues the ongoing Home Assistant template refactor by extracting the entity-related template helpers into a dedicated Jinja2 extension, keeping behavior and coverage equivalent while reducing the monolithic template module surface.

Changes:

• Added a new EntityExtension that provides entity_name (global + filter) and is_hidden_entity (global + test).
• Removed the legacy entity_name / is_hidden_entity implementations and manual registration from homeassistant/helpers/template/__init__.py.
• Relocated the corresponding unit tests from the template init test module into the extensions test suite.

Reviewed changes

Copilot reviewed 5 out of 5 changed files in this pull request and generated no comments.

Show a summary per file

File	Description
tests/helpers/template/test_init.py	Removes entity-related tests and drops now-unneeded registry imports.
tests/helpers/template/extensions/test_entities.py	Adds dedicated extension tests for entity_name and is_hidden_entity.
homeassistant/helpers/template/extensions/entities.py	Introduces EntityExtension implementing entity_name and is_hidden_entity.
homeassistant/helpers/template/extensions/__init__.py	Exports EntityExtension for extension loading by dotted path.
homeassistant/helpers/template/__init__.py	Registers EntityExtension and removes legacy function definitions and limited-template stubs for these names.