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I always assumed it was sort of like going into cryogenic sleep.
If a pokemon turns into data and is stored in a ball/PC, they don't really exist again until they come back out. So technically they'd experience nothing while inside. Just wake up again the next time they come out. Like storing data on a flash drive. All your secret fetish porn isn't having a constant coke induced orgy when it's not plugged it into your computer. It's just inactive until it gets turned on again.