Scale to zero is great. What happens when your app has to do something at 3 AM?

I've been thinking about the trade-off with serverless platforms like Cloud Run.

Scaling to zero sounds ideal for a small product: no traffic, no compute running. But real apps aren't always just HTTP requests. You have scheduled jobs, background tasks, webhooks, database connections, and work that shouldn't disappear halfway through execution.

How do you structure a real production app around scale-to-zero? Do you keep everything serverless, split workloads between services and jobs, or eventually move to something always running?

I'd be especially interested in hearing what worked (or surprised you) in an actual project.