I just stumbled on this question of yours: https://physics.stackexchange.com/questions/715474/on-shell-poisson-brackets-and-time-derivative
Your first equation (Liouville's equation) is: $\frac{\partial\rho}{\partial t}=-\{H,\rho\}\tag{1}$
But on the Wiki they define it as ${\displaystyle {\frac {\partial \rho }{\partial t}}=\{\,H,\rho \,\}}$
Why is the sign difference?