What would push complexity research forward? In my view, a greater concentration of empirical works would give this field more attention.

There's a useful YouTube channel by the Santa Fe Institute that broadcasts research in this field. Last month, there was a good presentation by Srividya Iyer-Biswas.

Based on the Santa Fe Institute's channel: "Iyer-Biswas and her team have reported predictive scaling laws governing the stochastic growth and division of cells, and have developed a theory that reveals the emergence of a scalable, cellular unit of time. Her current work involves extending these results to thermodynamics of organismal computation, time-dependent phenomena involving cellular decision-making, and laws that dictate complex biological and social phenomena."

If interested, the video is here: https://www.youtube.com/watch?v=wV1mWE8Zyi0.