core: script last_triggered not recorded/restored

The problem

While the automation last_triggered is recorded and read from history perfectly, the last_triggered for scripts isn’t.

I only noticed this because we can now set the secondary_info: last-triggered on entities of the domain automation and script.

Automations show last_triggered from weeks ago (if applicable of course) script always start with Never triggered after a restart…

Environment

• Home Assistant release with the issue: 105.5
• Last working Home Assistant release (if known): not known
• Operating environment (Hass.io/Docker/Windows/etc.): Hass.io
• Integration causing this issue: script
• Link to integration documentation on our website: https://www.home-assistant.io/integrations/script/

Problem-relevant configuration.yaml

  - type: entities
    title: Tradfri automations & scripts
    show_header_toggle: true
    entities:
      - entity: automation.tradfri_parking_light_shows_unavailable
        secondary_info: last-triggered
      - type: custom:toggle-lock-entity-row
        entity: script.reset_ikea_hub
        secondary_info: last-triggered
      - type: custom:toggle-lock-entity-row
        entity: switch.sw_everspring_no_template
        secondary_info: last-changed

automation shows correctly, script shows

Traceback/Error logs

no logged errors as far as I can see

Additional information

https://www.home-assistant.io/lovelace/entities/#secondary_info

before restart:

after restart:

just to be complete: yes, I have included both automation and script in the recorder and logbook settings.