You need to distinguish between a unit root and a singularity problem. Whenever you have a unit root you will get that message about collinearity in model_diagnostics. But that does not always indicate that there is something wrong. If the unit root is a feature of your model (like e.g. in the basic New Keynesian model where the price level has a unit root) then everything is fine.
You only have a problem if the unit root should not be there or if the Blanchard-Kahn conditions are not satisfied.