HA shutdown trigger: service doesn't preserve input changes

[ElStupid]

The problem

When creating an automation that runs at Home Assistant shutdown (or restart), setting an input boolean to a specific value doesn't work properly. Any input for that matter.

To test this: I did create a helper with input_boolean state set to off, no special configurations. I also created an automation to do the following

1. Push notification with the current state of an input_boolean helper
2. Change the value by calling service Boolean input: turn on
3. Push notification with the current state of an input_boolean helper

From the push notifications I see the value is changed, however not preserved after restart.
This also doesn't work with setting the value to off at first

What version of Home Assistant Core has the issue?

core-2022.8.4

What was the last working version of Home Assistant Core?

No response

What type of installation are you running?

Home Assistant OS

Integration causing the issue

No response

Link to integration documentation on our website

No response

Diagnostics information

No response

Example YAML snippet

alias: HA shutdown
description: ""
trigger:
  - platform: homeassistant
    event: shutdown
condition: []
action:
  - service: notify.mobile_app_me
    data:
      title: "System shutdown part 1"
      message: >-
        Home Assistant is shutting down. State 1st is {{
        states("input_boolean.recovery_state") }}
  - service: input_boolean.turn_on
    data: {}
    target:
      entity_id: input_boolean.recovery_state
  - service: notify.mobile_app_me
    data:
      title: "System shutdown part 2"
      message: >-
        Home Assistant is shutting down. State now is {{
        states("input_boolean.recovery_state") }}
mode: single

Anything in the logs that might be useful for us?

No response

Additional information

As discussed here: https://community.home-assistant.io/t/add-event-for-ha-restart-to-correctly-detect-power-loss/450087/20
The state preservation seems to happen before the event trigger?