Are you aware you're commenting on a nostalgic bluetooth kids phone which pairs to your mobile phone in the same way a headset does?
I'd consider myself 'aware' rather than 'paranoid', but if we extrapolate for a minute....Some function or app on the phone (or distant cloud service) can recognise the MAC address of the Fisher price phone's bluetooth PHY and, coupled with GPS info, we have a location where there's possibly a young child (or an older one in their home office!). Maybe, worse case, your targeted ads contain more children's toys.
That’s not how MAC addresses work. Once a packet crosses a router, the packet appears to come from the MAC address of the router.
So for example a web site you connect to has no idea what your MAC address is.
...unless you (or the app you're running) tells it.
But, yeah, you're not wrong for IP networking - however, an app on the phone could forward the MAC address of the bluetooth connected device.
But you are correct that regular apps can't address the MAC address of connected Bluetooth devices, so the tracking vulnerability that OP is suggesting isn't really possible.
"Connects to your mobile device with Bluetooth® wireless technology to make and receive calls through your existing phone plan—no additional line required (Compatible with IOS and Android™ devices)"
Calling random people doesn’t seem like something that’s a good idea.
The closest I could find to it saying that was the customer questions, one of which was answered with, “This one is intended for adult collectors.”