On Windows (and I assume MacOS too), you can move your cursor between multiple displays (both connected to the same computer). Is there a way, using third-party apps or natively, to allow movement of the cursor between the computers running the different OS's?
There are different solutions:
Software as Synergy[s] (multi-platform and open source) that allows to share a single set of mouse and keyboard (and clipboard) between different complete computers.
Once the program is installed, users can move the mouse "off" the side of their desktop on one computer, and the mouse pointer will appear on the desktop of another computer. Key presses will be delivered to whichever computer the mouse-pointer is located in. This makes it possible to control several machines as easily as if they were a single multi-monitor computer...
The computer has to be connected to the same network.
TCP/IP communications (default port 24800) are used to send mouse/keyboard and clipboard events between computers
It works as a client-server-service. So you have to install the server side on one and the client on (all) the other(s), with the same architecture of the following class of remote desktop software.
Remote desktop software: there exists a long list  of programs that can allow controlling remotely an OS as if you were physically logged to that machine.
They cost few in term of CPU usage (I can recall to memory nx  for example able to encrypt the flow efficiently).
The computers have to be connected to a network (at least a NAT, but they can be connected to the internet even in different countries) but it is not needed for them to stay in the same room.
So a solution can be to run your OS-es each on its machine, to connect both monitors to the most powerful one and from there to connect to the second machine via one of this software. (Note that with modern displays you can have more than one input channel so you can connect both computers to the same monitor and one computer to both monitors).
You will have your second OS in a window, but you can send it to the second monitor or to set it there directly. Then you can move your mouse between the screen and so between the systems.
Moreover, some of those programs may allow you to drag and drop element between the two separated systems, encrypt the communications... (Remember they are separated systems).
Just an idea. You can try to use a wireless mouse and to set two receivers (one for OS) to work at the same time (maybe you have to find a hack to make it works). Setting for example the first monitor between X=0 to X=1280 and the second between X=1281 and 2560 (if 1280 is the width in pixels of the displays) and allowing the mouse to go out of the screen on both systems... [I can see some problem if you drop (or the systems drops) some icons out of the screen part visually accessible... ]
One time there was the use of material switches to connect more than one computer with a single set of mouse/keyboard and even video.
In general, I like the idea of a mouse as a television remote control, with a narrow-angle to transmit the signal that can act in a similar way to the smart TV ones when pointing at them, they show the pointer on the screen. In my knowledge, at present, there is no yet a general solution that works in this way...