Preparing the next gravitational million-body simulations: evolution of single and binary stars in <tt> <scp>nbody6++gpu</scp> </tt>, <tt> <scp>mocca</scp> </tt>, and <tt> <scp>mcluster</scp> </tt>

We present the implementation of updated stellar evolution recipes in codes \texttt{Nbody6++GPU, MOCCA} and \texttt{McLuster}. test them through numerical simulations star clusters containing $1.1\times 10^5$ stars (with $2.0\times 10^4$ primordial hard binaries) performing high-resolution direct $N$-body (\texttt{Nbody6++GPU}) Monte-Carlo (\texttt{MOCCA}) to an age 10~Gyr. compare models implementing either delayed or core-collapse supernovae mechanisms, a different mass ratio distribution for binaries, white dwarf natal kicks enabled/disabled. Compared \texttt{Nbody6++GPU}, \texttt{MOCCA} appear be denser, with larger scatter remnant masses, lower binary fraction on average. The produce more black holes (BHs) helium dwarfs (WDs), whilst \texttt{Nbody6++GPU} are characterised by much amount WD-WD binaries. kick velocity escape speed distributions similar BHs neutron (NSs), some NSs formed via electron-capture supernovae, accretion-induced collapse merger-induced cluster all simulations. WDs, other hand, very dissimilar. categorise available \texttt{Mcluster} into four levels: one implemented previous versions (\texttt{level A}), state-of-the-art prescriptions B}), testing phase C}), those that will added future our codes.