You can log into your account on a different console, but it will be recognized as a "secondary" console for your account, meaning the games you bought can only be played by your user on this console, and it needs to connect to the internet every 4 hours or so to verify... well, I don't know what it needs to verify, but it does. Meanwhile, your primary console continues to work as always - that is, you can play games on it with any user, and while offline. You can also change which system you want to work as the primary one, though I haven't done it myself.
Right now, I'm sharing my account with a friend, and we've played Splatoon 2 together on multiple occasions despite it having only been purchased by one of us (me). We can't play if we both try to do it on the same user, but if I boot it up with another user (which I can because it's the primary console), it works perfectly fine - and thankfully, I've always used a second account anyway.
Edit: in short, don't worry about it. The 3DS sucked hard when it came to this kind of stuff, it fucked me over too. But the Switch does it fine.