MacBook connected to the iMac keep on disconnecting

**Setup** I've got an iMac on Ventura 13.5 with a connected Magic Mouse and a Magic Keyboard. I am sharing the Magic Mouse and the keyboard with another Mac (Ventura 13.5). The two devices are a foot apart, they both are connected to the same Wi-Fi, and both are signed in with the same Apple ID. The *Mac* has a second monitor connected to it via HDMI. ![Screenshot of the Display settings arranged in the following order: iMac MacBook, and Dell monitor ][1] **Problem** With increasing frequency, the iMac has started to randomly disconnects from the MacBook. Then, one will only see the image on the Display settings. This is rather annoying as I use the mouse and the keyboard to work on the MacBook. Edit : To add more clarity, the issue as far as I understand is that the Mac display gets disconnected. That is, I can only see the iMac under the displays in the attached image. As a consequence of this disconnection, the universal control fails too. **Attempted troubleshooting** 1. Updated both the iMac and the MacBook to Ventura 13.5 2. Switched off and switched on both the keyboard and the mouse. 3. I noted previously when I am in a Zoom meeting on the iMac, the MacBook gets disconnected from it. But I do not have Zoom open anymore.