Amazon Sidewalk means that PiHole or AdGuard won't stop anything, because the point of amazon sidewalk is that if a device can't find a usable internet connection (ie, you didnt set up wifi, or you dont have wifi), it can still function by connecting to nearby open networks, or perhaps even someone just walking by with a phone that it can piggyback off of.

So setting up a pihole prevents it from phoning home on your network, which will just prompt it to jump to another network potentially.

The question is just "how aggressively does this device want to phone home?" Some devices will actively seek out ways to phone home if blocked, some devices will try to phone home and give up if blocked. Some devices don't try to phone home at all.

Not phoning home is ideal, a pihole will (probably) keep a device that stays on your network under control, and you should just not buy things that actively will work around your intentions to do whatever it wants without your permission.

But this person has already bought the thing, so "dont buy it" isn't an option. But "don't use it" might be. Depending on which category it's in. (which I do not know, just trying to illustrate the bigger problem with Amazon Sidewalk)