As others have stated, the cleanest option for a single monitor setup is to either share a specific window, or start making use of multiple virtual desktops, sometimes referred to as workspaces. Windows, Mac, and Linux are all capable of it, now - the only difference is how you set up, arrange, and navigate them.
Linux options offer the most versatility, Mac’s implementation is a decent balance between ease of use and scalability (with caveats), and the Windows native implementation is the newest entrant to this playing field… but it’s an adequate offering that gets the job done for this use case.
I do, too, and drove one for many years. I’ll be the one to splash cold water on the conversation, though.
Driving a stick arguably requires the use of both hands and legs, which is great and partly the reason why so many enjoy it - that sense of engagement. It’s far less boring.
But here’s the deal. Injure any one of those appendages and driving a manual becomes a whole lot less fun. In some cases, you can get by, but it’s less than ideal. Having your arm closest to the shift in a sling, for example, makes your vehicle undrivable.
It won’t matter to most people… right up until the moment it does.