How is the Density Altitude performance penalty split between propeller and engine?
There is no reciprocating gas engine or gas turbine which is not affected by density altitude, the density of the air directly affects how much mass of working fluid can be taken in by the engine for a given volume of air and as a consequence the amount of power it can develop for a given fuel consumption.  The less dense the air, the less power or thrust the engine can develop.

Turbocharging or supercharging a reciprocating engine can maintain uniform power outputs for a throttle input provided the density altitude does not exceed the critical altitude of the turbocharger.  Turboprop and turboshaft engine are generally 'flat-rated' ie the fuel controller maintains a uniform power output right up to the thermodynamic rating of the gas generator at altitude.

As for propellors, the thrust they can deliver is directly proportional to the density of the ambient air, so higher density altitudes mean less thrust for a given power input from the engine.

Performance tables for both engines and propellors are available from the manufacturer and vary between make and models.  In general, pilots really don't use this as much as the aircraft performance tables in the POH for a particular aircraft.