When I need to have Google Assistant so something on HA, I can create a script in HA, expose it to Google Assistant (synchronize). From there I open my Google Routine, Add an Acfion, Add a Scene and if I did everything correctly I should be able to see/select the exposed script.
Is it possible to expose automations? Can Google Routines trigger HA automations? Having to create a script to run an automation is a bit silly.