How does a WiFi adapter work straight out the box?

So from the ones i've used, they can either have a default username and password enabled like:
username: admin
password: admin etc.
Or they don't actually even let you connect to the internet until you enter a username and password of your choice.

If you are able to connect to the internet, i'd say that it's got the default username and password option.
This is fine to get you going but to be secure it means you have to log into the router and change it to something new.

If you’re sure you can only access your router through a password, then you may be connected to a neighbor.

Not secure. If you can get in without a password, anyone passing by can do the same.

The unit could be one that's generic and doesn't require a password, but I would check my network and all connections and passwords. This doesn't sound right.

if its just hardware, then I'd expect that its its using the same network profile/ password from previous hardware, just through the new radio.

It’s just boosting the signal... but you still need to type in the home WiFi password