Add option to trigger template triggers when the template updates

[Petro31]

Proposed change

Currently, template triggers only trigger when the template previously renders false and then renders true. This limits template triggers and forces users to create template entities.

Adding the ability to optionally trigger off any template change opens up functionality for automations and template entities.

e.g. A user would now be able to create a trigger based template sensor where there's shared templates across states and attributes.

template:
- trigger:
  - platform: template
    value_template: "{{ states.binary_sensor | map('entity_id') | select('is_state_attr', 'device_class', 'battery') | select('is_state', 'on') | list }}"
    trigger_on_new_value: True
  sensor:
  - name: Binary Sensor On Entities
    state: "{{ trigger.value | count }}"
    attributes:
      entity_id: "{{ trigger.value }}"

Type of change

• [ ] Dependency upgrade
• [ ] Bugfix (non-breaking change which fixes an issue)
• [ ] New integration (thank you!)
• [x] 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: https://github.com/home-assistant/home-assistant.io/pull/33614

Checklist

• [x] The code change is tested and works locally.
• [x] Local tests pass. Your PR cannot be merged unless tests pass
• [x] There is no commented out code in this PR.
• [x] I have followed the development checklist
• [x] I have followed the perfect PR recommendations
• [x] The code has been formatted using Ruff (ruff format homeassistant tests)
• [x] Tests have been added to verify that the new code works.

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

• [x] 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 link to the changelog, or at minimum a diff between library versions is added to the PR description.

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