So they will scan the package, notice the phone, unpack and start it to check the battery percentage and if the shipping mode is enabled?

I hadn’t considered that possibility until you suggested it, but your question does make a good point. I’ll have to look up the mail inspection rules but I assume(?) they have every right until a court finds otherwise. It sounds like exactly the sort of overbearing, petty nonsense that one can reasonably predict from this decade’s administration of the U.S. federal postal service. Are they likely to do so every time? Absolutely not. Will they do so until they get to make an example of someone? Wouldn’t surprise me in the slightest, honestly.