Many projectors include remotes that allow you to control a slide presentation. These remotes send the default keystrokes that Microsoft PowerPoint knows (and which other presentation software copied) So when you connect a projector the OS often sees a keyboard and mouse. This triggers macOS’s keyboard recognition tool. Old VGA projectors had separate keyboard/mouse ports. I assume HDMI has a USB channel?

> I assume HDMI has a USB channel?

No, it doesn't, it only has I2C (for display identification and control, same as VGA and DVI) and CEC (for remote control).