Deprecate async_add_hass_job

[bdraco]

Proposed change

Deprecate async_add_hass_job

In #113260 we deprecated async_run_job and async_add_job. As we no longer have integration usage of async_add_hass_job we can deprecate it as well. async_run_hass_job should be used instead.

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: Add blog post about deprecating async_add_hass_job developers.home-assistant#2140

Checklist

• 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.

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

• Documentation added/updated for developers.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.
• Untested files have been added to .coveragerc.

To help with the load of incoming pull requests:

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

[bdraco]

We only have 3 places left where this is called. We should try to get rid of them so we can deprecate this as well

homeassistant/components/matrix/__init__.py:            EVENT_HOMEASSISTANT_START, handle_startup, run_immediately=False
homeassistant/components/rfxtrx/__init__.py:            dr.EVENT_DEVICE_REGISTRY_UPDATED, _updated_device, run_immediately=False
homeassistant/helpers/event.py:        run_immediately=False,

[bdraco]

event can be switched after #115160

If we can fix the other two we can deprecate run_immediately=False and get rid of this completely in a future PR

[bdraco]

codecov is likely going to fail.

Directly covered lines in core:
homeassistant/core.py 1092 93 91% 434, 459-467, 476-490, 528-532, 550, 819, 956, 1041-1045, 1062, 1064-1065, 1068, 1079, 1146, 1158, 1161, 1188, 1206, 1373, 1422, 1432, 1494-1496, 1510-1511, 1526-1534, 1602-1610, 1752, 1770, 1774, 1840, 1941, 1986-1989, 2030, 2075, 2122, 2348, 2398-2400, 2417, 2471, 2511, 2579, 2584-2591, 2636, 2642, 2736, 2773-2774, 2848, 2850, 2852-2855, 2865, 2889, 2972, 2981-3000, 3008

667-684 are the new lines here for the report and test coverage was verified locally

[bdraco]

This will go away in #115169