I dislike apple as a company but I have about 19 years of experience very much to the opposite of this claim.
Because Bluetooth is a separate hardware module than the CPU. “Sleep” is just a low-power state for the CPU, one of the “S” states. Other modules on the motherboard are still powered and can handle their own tasks, like Wake on LAN received at your network card, or keeping your RAM hot with your running programs.
Right. And it does so with minimal battery loss like any competent hardware in the 2020s. Most of the x86/64 world (Intel really) just can’t figure this concept out apparently. I’ve had a total of 1 PC laptop that did and it’s an AMD Ryzen 5000. That thing sleeps beautifully. I blame Intel for most of the weird issues people see.