core: Logbook.log doesn't show script entries since 0.112

Since upgrading to 0.112 I do not see my own logbook entries I use this service in many scripts.

Environment

• Home Assistant Core release with the issue: 0.112.4
• Last working Home Assistant Core release (if known): 0.111.4
• Operating environment (OS/Container/Supervised/Core): Home Assistant
• Integration causing this issue: Logbook
• Link to integration documentation on our website:

Problem-relevant configuration.yaml

include: entities: - alarm_control_panel.hmip_alarm_control_panel - binary_sensor.fkt_flur - binary_sensor.ftk_wz - climate.bad_jorg - climate.bad_yvonne - climate.fitnessraum - climate.gastewc - climate.gastezimmer - climate.schlafzimmer - cover.rolladen_kuche - cover.rolladen_wohnzimmer - light.gastezimmer - light.fitnessraum - light.office - light.kuche - light.wohnzimmer - light.schlafzimmer - light.gartenleuchten - person.jorg - person.yvonne - remote.wohnzimmer - switch.kuchenlicht - switch.luftbefeuchter - switch.ventilator - switch.zone_1_zone

    - service: logbook.log
      data_template:
        name: "Rain_delay_on"
        message: "has been activated"

and

script:
add_log:
  sequence:
    - service: logbook.log
      data_template:
        name: "{{ name }}"
        message: "{{ message }}"
```

## Traceback/Error logs
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`no logs

```

## Additional information