Help on creating a USB Hub Switch that enables multiple computers to share USB device?
The idea here is if I connect a mouse to the switch all 3 computers will know that a mouse is connect and ready to use however only the chosen computer will actually receive the data send by the mouse, avoiding this way extra awaiting time when switching a device between computers.

That is not as easy as you think: A host polls every USB device several times a second. It has to respond, otherwise it's proclaimed dead and the bus is reset.
So, you need to have something between computer and, say, mouse that emulates an idling mouse &quot;upwards&quot; for all but the one PC that's &quot;active&quot;. Problem is that a mouse, a keyboard, generally devices, are stateful things, so you need to really be continuous in your emulation.
In other words: there needs to be a computer sitting in your &quot;switch&quot; that looks like the specific USB input devices to one side, and like a host computer to the other, and does all this handling.

avoiding this way extra awaiting time when switching a device between computers.

Software problem. Solve in Software. Plugging in a mouse into a computer has never took longer than a second for me until it was ready to be used – are you perhaps using Windows XP or something?

The higher the usb specification the better, 3.1 would be ideal.

Absolutely not. Either you emulate mice, or you pass through USB 3.1.
Also, the devices that actually use USB 3.1 are almost all large mass storage media. You can't just &quot;unplug and replug&quot;, you need to unmount/&quot;safely remove&quot; or this will, very soon, end in a big disappoointment when you notice there's write caches on your computers. If you want one place to plug in your USB3.1 storage media (external SSD/hard drive/thumb drives) and access them everywhere, that would simply be some network-attached storage. Seeing that USB 3.1 is significantly faster than Gigabit Ethernet, this might need some requirements modelling. I'm sure there's companies willing to sell you 10 Gbit Ethernet NAS systems...
There might be a couple USB2 Hi-Speed, maybe even USB3 SuperSpeed cameras, but they have complex firmware, meaning complex state. You can't just &quot;switch over&quot; these, either.
So, what you want (USB input device emulation in parallel to USB3.1 10Gb/s passthrough) is impossible. What can be done, and is done by the better KVM switches, is emulating input devices upstream; that can be bought. But honestly, the problem you're describing sounds like you should use an operating system that doesn't make you wait after it detected a mouse that it saw yesterday already.
By the way, for &quot;quick&quot; changes between computers, people tend to just have one workstation and use remote desktop methods to log into the others. Unless your PCs differ by hardware very much, I'd also recommend looking into what modern Virtualizers can do – there's no reason you'd need a separate PC to run a Windows for your bookkeeping software on your Mac, for example, or boot into Linux just to get a proper development environment.