Confirm/critique my thoughts on information and entropy

I would like for someone to review and confirm or critique my thoughts on the relationship between entropy and information. My thoughts are oriented towards large "brush strokes" rather than fine, minute detail, as I am not very well versed in the technicalities of physics, specifically, in thermodynamics and information theory. Here, summarized in my own words, is what I have gleaned from various sources:

As entropy increases in a given system, the number of possible microstates that exist for the particles in that system (which obviously, do not affect the system’s overall macrostate) increases.

Thus, as entropy increases in a given system, the less information we have about the physical states of the constituent particles of that system.

However, as entropy increases in a given system, the more information this system has, as the total number of possible microstates for its constituent particles increases.

So here is the paradox: as entropy increases in a given system, the less information we have about that system, but the more information is contained within that system. So when physicists talk about information being "lost" as the universe marches on its inexorable path of entropy, are they referring to the information we have about the universe?

Are my thoughts correct? If not, where have I erred?