Now we're getting into the semantic games. I know you'll likely come back with some attempt to say, "Ahhh, but acktually..."
I'll bite anyway.
As far as
most people would accept it, for as long as consoles have existed, here's a rough stab: it would be a non-upgradable piece of somewhat customized hardware, using a custom set of sdks, apis, and dev tools provided by the manufacturer; the OS is a custom OS and is completely closed for installing a user's own choice of applications and games, all games and applications must be installed via only manufacturer accepted methods. The OS cannot be reasonably customized, or replaced without significant effort/hacking. Publication of games must pass through the manufacturers approval process and contractual terms. Unless emulated, games will not run on other computing systems. You cannot connect external peripherals unless they are approved and have manufacturer drivers. You cannot add new drivers because of the OS restrictions stated above.
A steam deck meets the critera of the hardware isn't easily customizable/replacable, but outside of that, you're not restricted in any way whatsoever. If you want windows, install windows. If you want to write your own OS to put on there, you can. If you want to create your own games on it, you can. If you want to use it as a web dev box, you can. You can run pretty much any PC game going back to the beginning of PC on it. You can install emulators and run whatever you want. You can run DOS on it. You can connect any peripheral to it you want. You could write new drivers for hardware you created yourself, and publish those on a linux package manager and publish that, and let anyone use those things. None of that is possible with the established definition of console.
It is
console-like in that it borrows the ease of use focus from consoles, its big picture mode and interface aren't complete shit without a mouse and keyboard like Windows is, and it is a single set of hardware atm, but there are many Deck-likes that run exactly the same thing.
I think everyone has a pretty good idea what a traditional-model console is, and the XBOX, Playstation, and Switch follow that definition. Standalone VR sets like the Quest are close, and maybe fit the definition. The iPad is kind of straddling it. The Steam Deck is, IMO, not a console.