Is supercriticality dependent on partial presssure, or total pressure? Supercritical CO2 is commonly used as a solvent in organic chemistry (notably in industrial processes like decaffeination). I presume that in such cases, the CO2 is typically pure, or very close to it.

But suppose you had a mixture of, e.g., 50% CO2 and 50% nitrogen. Pure CO2 becomes supercritical at approximately 31C and 73atm; particularly in terms of its solvent properties, would the CO2 in that mixture also demonstrate supercritical properties at 73atm total pressure, or would it be necessary to double the total pressure, producing 73atm partial pressure of CO2? Or is the interaction more complex than that, with mixture of CO2 and N2 having a joint critical point different from either single gas?
There is no such thing as supercritical properties. By looking at a gas under given pressure and temperature, you'll never be able to tell is it supercritical or not.

If you try to lower temperature or pressure and see what happens, then yes, the interaction is more complex, and a mixture of two compounds does indeed have a joint critical point different from those of both pure compounds; moreover, the very meaning of a critical point becomes different and more complicated.