But does it automatically recognise it as an SSID and password and connect as the website suggests?

On iOS, you get a banner notification with the name of the wifi network, for you to tap to connect to. It does the rest from there, yes.

This has been the case for quite some time. I assume Android can do it too (and if so, probably did it first).

My Samsung S20 can. IDK about other phones.

Yes