I picked up the base model Mac Studio with M1 Ultra on Friday and have had no issues with Bluetooth using the Apple keyboard and mouse. The only thing that I have noticed is that after a reboot of the Mac Studio, it takes several seconds for the mouse to connect. In other words after the Mac Studio is booted, you can click the mouse to wake it up and start moving the mouse around, but the cursor on the Mac doesn’t start moving for about 5-6 seconds, which seems like an eternity when you’re waiting to log in.
On another note, the only time I have experienced any Bluetooth issues is in my vehicles. Occasionally it will disconnect for some unknown reason and sometimes it won’t reconnect until I restart the iPhone or the vehicle’s audio system. Other than that, Bluetooth has been flawless on all of my computers.