Not interrupts but SLEEP or NAP. Interrupts keep the clock running but with SLEEP and NAP it all shuts down for a selectable period of time, wakes up, does its thing and goes back to sleep.
The data sheet I saw said 1uA at 3.3V so you may get down that low if you work at it.
It also looks like this chip has LED driver pins. Maybe you should look at a different chip for your more specific needs.
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