Reconnecting Mac to new home wifi

You can tell the Mac to forget the network by going into Setting > Network > WiFi > [Network name] > Details > Forget this network. You might also be able to use the Advanced option in the Wi-Fi panel, select the name of the network under Known Networks, and from there use the circle with the dots button to bring up a list of options and choose the one called Remove From List. This ought to have the same result.

Your question is a bit contradictory. On the one hand you say that your Mac auto connects to your network but also that you have a new password preventing your Mac connecting?

Would this be an NBN fibre connection to your home, with a new ISP modem?

With new equipment a network name would usually be expected to be new and with a new password. How did it come with the same password as your previous modem? Also, you can connect to a local network and still be off the Internet. Have you tested the Internet connection with any other device?