Differentiating license issues with connection issues

We're running matconsolectl in a server job and using a corporate license pool.
Sporadically, we're getting this exception:

Exception in thread "main" matlabcontrol.MatlabConnectionException: MATLAB proxy could not be created in 180000 milliseconds
at matlabcontrol.RemoteMatlabProxyFactory.getProxy(RemoteMatlabProxyFactory.java:176)

I suspect that this is caused by being out of matlab licenses, but as far as I can tell from the matconsolectl source code, it does not have any special handling of license issues compared to e.g. network issues. Or am I misdiagnosing this and license errors will not get MatlabConnectionException timeouts?

It would be really nice if one could get the error message we get when running matlab directly, i.e.

"License checkout failed.
License Manager Error -4
Maximum number of users for MATLAB reached.
Try again later."

I'm not sure where to start looking for the above output though, so not sure how to fix it (if this really is the issue that I think it is)

Start at RemoteMatlabProxyFactory.java:176 and trace how proxy-creation timeouts surface through the matconsolectl source. Reproduce the license-exhaustion case if possible, compare it with a network failure, and identify whether the MATLAB license-manager message is available; done means the two failure types are distinguishable or the limitation is documented.

Written by the indexing model from the issue text.