Can I split the feed to a duplex 20 amp receptacle from different capacity circuits?
No, you can't feed a split receptacle from circuits with differently-sized breakers. Here's why:
You can, but you have to meet certain conditions:

The National Electrical Code now requires that the two hot wires in a split receptacle must be connected to a double-pole circuit breaker, so that when the breaker is shut off, the action will automatically disconnect both receptacles. That way, the outlet will be safe to work on.
source: The Spruce

To my knowledge, handle-tied double breakers with different current ratings don't exist. However, as ThreePhaseEeel points out, you may be able to find UL listed handle-ties for your breaker brand. This would require that they be mounted adjacent. Or you could reduce the 20A circuit to 15 Amps and use the same wire.