Mosek via cvxpy - save verbose output

Question

I use Mosek through the cvxpy interface. When I use the verbose option, it shows some nice output, that I would like to further work with. I looked through the parameters in https://docs.mosek.com/latest/pythonapi/parameters.html#doc-sparam-list whether something would store me this output somewhere. The parameter stat_key seemed promising, but it does not work as I thought.

MWE:

import cvxpy as cvx
import mosek
import numpy as np

A = np.random.randint(10, size = (16,32))
b = np.random.randint(10, size = 16)
c = np.random.randint(10, size = 32)

x = cvx.Variable(32, integer = True)
prob = cvx.Problem(cvx.Maximize(c @ x), [A @ x <= b, x >= 0, x <= 10])
prob.solve(solver = cvx.MOSEK, mosek_params={mosek.sparam.stat_key: 'results.txt'}, verbose = True)

expected/wanted behaviour: There should be a file results.txt that contains the line that are printed on the terminal from the verbose option.

observed behaviour: No such file exists.