In the Fortran code maxknn represents the "maximum number of neighbours to explore+1".
In duly, for self.maxk, we sometimes adopt such convention (in particular when the code has been copied slavishly from the Fortran code); some other times, like in the documentation in _base.py, we take maxk as the "maximum number of neighbours to be considered for the calculation of distances", which is one less than in the Fortran code; some other times we even take maxk to be the maximum kstar, which is different from the two previous. In fact kstar[i], according to both codes and to the JCTC2018 paper, represents the number of points counted to compute the kNN density of point i divided by the volume corresponding to the kstar[i]-th neighbour of i, which is however excluded from the counting.
We should adopt a common convention throughout the whole package. Please discuss