The maximum information capacity of a radio antenna is limited by the surface area enclosing the antenna. One could theorise that that in addition to a maximum density of information storage there will also be a limit on the error free rate at which information can be sent to/from a storage system system, probably related to the surface area enclosing the system.
Well under normal conditions (no degenerate matter)- the material with the lowest molar volume should give a good idea. At least on earth, this happens to be diamond: so ~1.7 * 10^20 atoms / mm^3.
I think we would be in trouble way before that. Quantum effects would mean you would change a decent percentage of adjacent bits while setting one. We’re probably struggling with such effects already.