How long can Prius C be idle?

there's no exact time. more than a week or two, and i would put an inexpensive maintainer on the 12 volt.
for the hybrid battery, it depends on age and health. i would start to be concerned around 6 months, and more concerned if it were a regular thing, like a vacation home or some such.
these cars like to be driven

 

Ones and Twos can sit longer due to basic ignition keylock systems. Threes and Fours don't last as long because they use smart key systems.

Endurance slides with age and temperature.

The hybrid battery has a finite lifetime, idle or used.

From an economic standpoint, the best you can do with a Prius is run the wheels off it from the moment you inherit one until the day before it becomes a money pit. For that one? You're probably good through 2025 whether you drive it or not.