Bluetooth lag after wake up from sleep on OS X Ventura

I'm running OS X Ventura 13.1 on a Mac Book Pro 16-Inch 2021 with M1 chip. Usually, I have my keyboard (Keychron K8 Pro), my mouse (Razer Naga Hyperspeed), and my headset (Bose Quiet Comfort 35), all three connected via Bluetooth to the mac book. All works fine without any issues, till my mac goes to sleep. When I wake up the mac all the 3 devices are still connected via Bluetooth, but they lag a lot. The mouse pointer is super laggy, and in the music there are interferences. If I shutdown Bluetooth or kill the process with sudo pkill bluetoothd all return to work fine. This is quite annoying.

Question by Pioz on Super User, licensed CC BY-SA. We show a short excerpt and link to the original thread as credit.