I can suggest 2 work around which will need 2-3 button pushes...

1. get a 1 or 2 computer (single or dual monitor) KVM that will switch between 2 computers and 2 monitors.
2. get a 2-3 computer HDMI switch (3 to 1 HDMI splitter) and use it to manage the 3rd input.

Advantage:

1. less costly
2. you can customize your devices
3. you can have 2 screens from PC 1 on 2 monitors, 3rd monitor can have 1 screen from the PC, e.g work PC on 2 primary screens, baseball game on 3rd screen from personal PC.
4. if you get the HDMI splitter with PIP function, you can overlay your personal PC screen on the 3 rd screen over your Work screen

Disadvantage

1. More wires
2. need to press 2 buttons
3. not as elegant as a proper 2 PC 3 HDMI KVM

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Option 2:

1. Get 4x2 HDMI multiplexer (instead of KVM) for 2 monitors.
2. Get a 2x1 HDMI multiplexer for 3rd screen
3. Get Logitech MX Keys KB and MX Mouse. They can switch between 3 PC at the press of button.

Advantage:

1. More control on what is shown on each screen

Disadvantage

1. More wires
2. need to press 5 buttons
3. not as elegant as a proper 2 PC 3 HDMI KVM

This HDMI 3 switch port, you could use a similar product, but this particular one switches between inputs depending on what's powered on.