When I say "scale to zero" I mean like Cloud Run or AWS Lambda: I define it as the service automatically scaling to zero (and hence costing nothing to run) in between requests, but automatically starting up again when a new request comes in - so the request still gets served, it just suffers from a few seconds of cold-start time.

I'm pretty sure Fargate doesn't offer this. It sounds like you're talking about the ability to manually (or automatically through scripting) turn off your Fargate containers, then manually turn them back on again - but not in a way that an incoming request still gets served even though the container wasn't running when the request first arrived.

Curious, have you used Cloudflare Workers Unbound to see how it compares with Cloud Run in terms of pricing and cold starts?

I haven't yet - my projects (all based around https://datasette.io/) need full Python support, and it looks like Cloudflare Workers still only with with JavaScript or stuff-that-compiles-to-JavaScript. I don't think I can get Datasette working via the Python-to-JavaScript route, it has too many C dependencies (like SQLite).