An interesting fact is that while almost all solid objects that exist in the Solar System have their origin in the condensation of gases from which the Solar System has formed, there exist also the so-called pre-solar grains.
The pre-solar grains are microscopic crystals, i.e. particles of dust, which have come to the Solar System as already solid grains of dust, from other stellar systems, typically having been propelled by stellar explosions, e.g. those of supernovae.
Such pre-solar grains have been incorporated in the many small bodies that have been condensed from gases along with the bigger asteroids and planets at the formation of the Solar System.
Some of those small bodies have fallen on Earth as meteorites (the so-called "chondrites"). When such meteorites have been analyzed carefully, pre-solar grains have been recovered. They can usually be easily distinguished from the local objects, by having very different isotopic compositions.
Among the pre-solar grains, there are many that have come from stellar systems of the second kind, with more carbon than oxygen. Such grains, instead of being silicates, i.e. the most frequent minerals in the stellar systems of the Solar type, have chemical compositions that are unusual for the minerals of the planets of the Solar System, like diamond, graphite, silicon carbide or nitride, titanium carbide or nitride, metal grains of either platinum-group metals or iron-group metals, other carbides, nitrides, sulfides, silicides or titanides.
For now, this is the only direct evidence of the second class of stellar systems, beyond the spectroscopic observations of various stars, which provide estimations for the relative abundance of carbon and oxygen in those stellar systems.
While we have some idea about what kind of minerals might be the most abundant in such stellar systems at the time of their initial condensation from gases, I am not aware of any attempt to simulate the possible internal structure for big planets in such stellar systems, in order to determine whether in such planets there could exist some analogs of the volcanism and hydrothermal vents that can provide the energy flux necessary for the appearance of life in the planets of the terrestrial type.