The New Generation Planetary Population Synthesis (NGPPS). V. Predetermination of planet types in global core accretion models

State-of-the-art planet formation models are now capable of accounting for the full spectrum of known planet types. This comes at the cost of increasing complexity of the models, which calls into question whether established links between their initial conditions and the calculated planetary observables are preserved. In this paper, we take a data-driven approach to investigate the relations between clusters of synthetic planets with similar properties and their formation history. We trained a Gaussian Mixture Model on typical exoplanet observables computed by a global model of planet formation to identify clusters of similar planets. We then traced back the formation histories of the planets associated with them. Using cluster affiliation as labels, we trained a Random Forest classifier to predict planet species from properties of the originating protoplanetary disk. Without presupposing any planet types, we identified four distinct classes in our synthetic population. They roughly correspond to the observed populations of (sub-)Neptunes, giant planets, and (super-)Earths, plus an additional unobserved class we denote as "icy cores". These groups emerge already within the first 0.1 Myr of the formation phase and are predicted from disk properties with an overall accuracy of >90%. The most reliable predictors are the initial orbital distance of planetary nuclei and the total planetesimal mass available. Giant planets form only in a particular region of this parameter space that is in agreement with purely analytical predictions. Including N-body interactions between the planets decreases the predictability, especially for sub-Neptunes that frequently undergo giant collisions and turn into super-Earths. The impact of gravitational interactions highlights the need for N-body integrators for realistic predictions of systems of low-mass planets. (abridged)