Ah, no. It’s the bound fix(M[i, j], 0). Just try removing that line.
Here’s the example with SCS
using JuMP, SCS
n = 150
model = Model(SCS.Optimizer)
@variable(model, P[1:n])
@variable(model, M[1:n, 1:n], PSD)
@constraint(model, [i=1:n], M[i, i] == P[i] - 1)
@objective(model, Min, sum(P))
@time optimize!(model)
@show termination_status(model)