Yeah, I don't know that there's such a jump. Dogs, for example, clearly communicate, both with us and with each other. They don't have language, but they also don't lack communication skills. To me, language is just "better communication" rather than a qualitatively different thing.
You may want to watch this video: https://youtu.be/e7wFotDKEF4?is=bl5TPvk9_mdnG3Om
Human language is way above what communication animals show. We don't really know what's the exact boundary, but again, the difference is significant and not just "scaled up".