Earlier quoted context omitted.
Does the Cloud Functions solution meet your current performance requirements? If so, don't worry about moving it. The main benefits you'd see immediately are toolchain (e.g. Docker containers, existing build systems, etc.).
I haven't launched it, so I'm not sure about performance. My main concerns are cold starts and concurrency. It's my understanding that Cloud Run has higher concurrency per container instance, so my guess would be that Cloud Run would give me fewer cold starts than Cloud Functions. However, since Cloud Run is a generic runtime, I'd imagine that cold starts there would be on the scale of seconds compared to millisecond…
I'd encourage you to test your particular app, but you should expect similar cold start times in Cloud Run.
You can set "Maximum Requests per Container" on container deployment so you are in control whether a container has single concurrency (i.e. "Maximum Requests per Container = 1"). If your app is not CPU-bound and you allow multiple concurrent requests (the default) you should see fewer cold starts.