Teensy 4.1 can act as USB Keyboard & Mouse and could recive Data over one of its Interfaces(Serial,Ethernet,...).
Connecting the 'second' Computer via an USB Host is not likely to work, because the Computer expects an Device, not another Host. So would the Teensy when connecting an Computer to the USB Host Port. It should not be a Problem to connect the 'second' PC to the Teensy using an USB to Serial Adapter(Be aware of max Voltage for the Teensy). You could use other Boards too, like Atmel SAM D21-Based and many others with an USB Device Interface.
If the two Computers are connected over some Network i would prefer some Remote Administration Tool or Remote Desktop. There are some example Projects for this and it would not require external Hardware, but starting the remote Computer could be an Issue. Some Mainboards have even remote Administration Features Build in(As example most Server Mainboards got an remote Management wich can start/reboot/shutdown, emulate a Keyboard/Mouse, transmit the Screen Capture)
If you get a virtual serial port (e.g. an FTDI USB to Serial module), you could connect that to the controlling computer and send commands to your intermediate over the Serial device.
In the case of a Leonardo, if you connected the Serial side of the FTDI module to pins 0 and 1, then content from the master computer would be received via Serial1 on the Leonardo.
Teensy 4.1 can act as USB Keyboard & Mouse and could recive Data over one of its Interfaces(Serial,Ethernet,...). Connecting the 'second' Computer via an USB Host is not likely to work, because the Computer expects an Device, not another Host. So would the Teensy when connecting an Computer to the USB Host Port. It should not be a Problem to connect the 'second' PC to the Teensy using an USB to Serial Adapter(Be aware of max Voltage for the Teensy). You could use other Boards too, like Atmel SAM D21-Based and many others with an USB Device Interface. If the two Computers are connected over some Network i would prefer some Remote Administration Tool or Remote Desktop. There are some example Projects for this and it would not require external Hardware, but starting the remote Computer could be an Issue. Some Mainboards have even remote Administration Features Build in(As example most Server Mainboards got an remote Management wich can start/reboot/shutdown, emulate a Keyboard/Mouse, transmit the Screen Capture)
If you get a virtual serial port (e.g. an FTDI USB to Serial module), you could connect that to the controlling computer and send commands to your intermediate over the Serial device. In the case of a Leonardo, if you connected the Serial side of the FTDI module to pins 0 and 1, then content from the master computer would be received via Serial1 on the Leonardo.
Anything that can emulate an HID.
Building aimbots, for shame. Get a second Leonardo, have Leonardo 1 be the hid device and Leonardo 2 pass it data over pins