Is there a Maximum Data Density of a Physical Volume?

The limit you want is the https://en.m.wikipedia.org/wiki/Bekenstein_bound bekenstien limit. This limit states that the amount of information a given volume can contain is proportional to the surface area of that volume. Specifically it is 1 bit of information for every 4 plank areas.

Note that because the limit is a surface area proportional to $r^2$ and the volume is proportional to $r^3$ where r is the radius, large volumes must be less information dense then is possible for some smaller volumes. With the limit of information of the universe identified with the "edge" of the observable universe.

Another way to understand this is if you try to push information smaller then this then you will condense it into a black hole with the event horizon being the correct area.