Something that may be coming into play (maybe), because Nintendo does a thing:
If you have the same account on two switches, one will be the "primary" switch and the other secondary switch. Any switch that isn't primary will require internet verification before it can start a game. Under normal circumstances to fix this, you can use a browser, login to your nintendo account, and assign your current switch as the primary.
Since this is a used switch, and it used to have the old person's account on it, it may be set to secondary? maybe? even after a format? I'm not sure how it works. It may be completely irrelevant, thought it was worth a mention. It was a bother with my two switches, and took me a while to figure out why one always needed internet to check before a game could start. Not sure how it decides on secondary accounts or when it releases them.