It's looking like the answer is no ☹️ but is there any way to customize how the state_content is rendered in badges (or other built-in cards, for that matter)?
As an example, I'm including the last_triggered state on this badge, but it ends up taking up a lot more space by writing out 19 hours ago when it'd be great if I could use a template to render this as 19h, or even make this count down down instead (since the action triggers something after a delay). There seems to be state_filter that can let you build relatively complex logic for whether the badge shows up or not, but seemingly nothing to customize how it actually shows up when it does.
From what I can tell online, it seems like the general solution is to create template sensors for everything and do the customizing there, but having two entries for every entity and wiring up the actions etc. gets gross pretty fast. 😬