Is there a way to accomplish v1's "Manual trigger"-like behaviour in Prefect 2.0? I mean, flow goes to paused state, and then with some interaction user can resume it?

Not directly but you could accomplish a similar solution using orchestrator pattern or by looking up some APPROVAL variable in a JSON block. If this feature is important to you, check if there's already a feature request for it in GitHub issues and if not it's totally fine to create it.