Feature (#1132) - Live-check: builtin output rendering for json, jsonl and yaml.

Added an OutputProcessor to weaver_forge which handles json, jsonl, yaml for builtin formats, templates or mute (no output).

The end goal is to unify all weaver output in a standard way. This first PR tackles this only for Live-check only.

A follow-up PR will fit this for other commands: diff and resolve.