Which computer owns the screen your work laptop records?

Start at the monitor's input menu, because that is the only thing the panel actually knows. It shows one video source at a time, and the computer driving that source is the one whose desktop you are looking at. Whether a recorder captures that desktop is a separate question, answered by software on each machine rather than by the cable you unplugged. Walk the four steps below in order: input, peripherals, software bridge, then the written boundary.

Start with the monitor's input, not the desk

Open the input selector and note which port is active: DisplayPort from the work dock, HDMI from the personal tower, or a USB-C input carrying both video and data. That answer tells you which machine is currently painting pixels, and nothing more. The other computer may still be running its own session, with its own recorder, on a desktop nobody is watching.

A switch that changes inputs does not suspend the machine that lost the display. Its session continues, its agent continues, and its screen state is whatever it was before you pressed the button.

This is why "the monitor was showing my home PC" is not by itself an answer to a monitoring question. The work laptop can be recording its own desktop while its output goes to a port nothing is displaying. Conversely, a recorder on the personal machine has no business capturing a work desktop it never renders, unless something copies that content across. The input selector settles ownership of the picture, and that is all it settles.

Follow the USB cable to the computer that owns it

Keyboards, mice, headsets and cameras complicate the picture because many switches move USB devices along with the video. Find out which computer enumerates each peripheral when the switch is in a given position. Some switches move everything, some move only keyboard and mouse, and some emulate a keyboard so the host never sees a disconnect.

Get-PnpDevice -PresentOnly -Class Monitor,USB | Select-Object Class,FriendlyName,Status
lsusb

The first command lists monitors and USB devices the Windows host currently sees, and the second does the same on Linux. Run it in both switch positions and compare. A headset that stays attached to the work laptop in both positions is a device the work session can still use, and a camera that moves with the switch is one it loses.

Check the switch's own documentation rather than inferring from the picture. Vendor manuals state which ports follow the selector, whether audio is switched, and whether the switch emulates HID devices. That detail decides whether the work machine believes a keyboard is present when you are typing on the other desktop.

Audit the software bridge, not just the hardware

Software sharing is the part people forget, because it leaves no cable to trace. Keyboard-and-mouse sharing tools move input, clipboard content and sometimes files between machines over the network. Microsoft's Mouse Without Borders documentation describes clipboard sharing and file transfer alongside input control, which is exactly the shape of bridge that turns one desk into one shared surface.

Remote desktop sessions, mapped drives and clipboard sync tools do the same thing at a larger scale. Once personal text or a personal file arrives on the work computer, the work environment's rules apply to it, whatever monitor was showing when it started.

So list the bridges explicitly: input sharing, clipboard sync, file transfer, remote desktop, cloud drives signed into both machines. Then decide, per bridge, whether it belongs on managed equipment at all. A tool that is convenient on two personal machines is a policy question the moment one of them is the employer's. Write the list down, because the bridge you cannot name is the one that moves a file while nobody is looking.

Write down the boundary you actually traced

Produce a short record with four lines: which computers have the agent installed, what that agent is configured to capture, which hardware and software paths cross between the machines, and what the organization's notice says about those capabilities.

Ask the responsible administrator to confirm the capture scope rather than assuming it. Disconnecting a VPN does not stop local recording, and a shared panel does not mean one agent sees both desktops. Both assumptions are common and both are wrong. The question to send is narrow and answerable: which sources does the agent on this asset collect, and which of them are screen-based?

The goal is a separation you can describe out loud: the work session stays inside its permitted monitoring scope, and personal content is not copied into it by accident. A switch button cannot certify that, but neither does a shared screen automatically merge the two computers into one.