The Switch is a handheld portable that can be connected to a TV, not a home console. I can connect my iPhone to my TV too, but its still a mobile device, not a home console. (And the Switch Lite cannot connect to a TV.)
Gameboy, DS, PSP, Switch, etc.. They're handheld portables (aka gaming centric mobile devices). Internal batteries, built-in displays & controls, etc.
Home consoles require a separate external display. And use an external controller too, wired or wireless. Like PS4, PS5, Xbox One, Wii, etc. They don't have an internal battery that needs recharging and allows for wireless use. They have fixed power supplies and must be plugged in to work. Unlike a phone or tablet (or Switch.)
Calling the Switch a home console is like calling a laptop a desktop.