Or, another possibility is that the sustainability of continuous short-term exponential growth varies from location to location but it's not going to be infinit

Or, another possibility is that the sustainability of continuous short-term exponential growth varies from location to location but it's not going to be infinitely sustainable anywhere. Thus we might see blips but we won't see a "colonized galaxy". IE, the societies that keep up exponential growth to a cosmic scale probably still won't have solved the problem of indefinite exponential growth. We know the ways that, on Earth, the increase in human knowledge and productive produces unintended consequences with significant chances of destroying us. We don't yet know similar mechanism in space but it seems quite plausible these would exist. Dyson spheres aren't even gravitationally stable (see Larry Niven's Ring World series).