ϵ = 10^-4;
R = Rationalize[1.5472, 0];
    sol = ParametricNDSolveValue[{y''[r] + 3 y'[r]/r == Sinh[y[r]],
        y[ϵ] == y0, y'[ϵ] == 0, WhenEvent[r == 1, y'[r] -> y'[r] + 32001/40]}, {y, y'},
        {r, ϵ, R}, {y0}, Method -> "StiffnessSwitching", WorkingPrecision -> 30];
    ff = FindRoot[Last[sol[y0]][R], {y0, -12.25, -11.}, Evaluated -> False][[1, 2]]