Your partner needs to change the home console on their account to the one you play on. Then you'll be able to play with different accounts. Usually most people

Your partner needs to change the home console on their account to the one you play on. Then you'll be able to play with different accounts. Usually most people only have one Switch so this never is a problem. However, if you've switched consoles and you didn't do System Transfer, you need to manually switch over the home console in order to get your offline play rights back. Alternatively your partner may have explicitly set their home account to someone else's system. There's a mildly pirate-y[0] thing you can do with a friend where you log into your account on their system and they log into your system with their account, and then you have a shared game pool. In order to be able to play on your own account you need to swap the home console associations around so your friend's Switch is your home console and vice versa. But if you do this you can never play your own games on other accounts, since your friend's the one who took that half of the license. [0] As in, it bends the rules of the DRM in ways Nintendo probably does not intend and thus probably violates a license agreement somewhere