For anyone else landing here after searching for “HomeAssistant automation cooldown” …
I found that last_triggered doesn’t work, because when it evaluates that condition, the attribute has already been updated to now(). So it never evaluates to true and the automation won’t run.
Instead, I ended up adding a timer as described in another post – add a Delay as the last action, and make sure the mode of the automation is set to “single”