At this point, the distinction between console and PC comes down to the corporate side. The PS4 and PS5 operating systems are based on a BSD (probably FreeBSD but not sure), and are capable of running a desktop OS (as long as hackers find a way to bypass Sony’s locked-down firmware). XBox One and Series use a Windows-based OS, also locked down by Microsoft to only run the applications they want.
Everything about the Steam Deck is designed with gaming in mind, but in terms of capabilities, it’s no different from a PC. You could hook it up to a USB-C dock and use it for work. I’d sooner call it a handheld PC than a console.
They don’t. It’s the same category as jailbreaking an iPhone: possible, legal, might brick your console, Sony hates it.