@Okay
You are correct that your member centre password is the same as that needed in the router settings to connect to the internet. If your router is a Plusnet supplied one it should be linked to your account and, if all is working correctly, any password change in your member centre should be sent to the router automatically.
If you want to ensure that you are prepared for the future should "things go wrong" (and you are actually in a state where your route password has not updated to match any changed member centre password) you could change your member centre password again now and, if the router does not update (or is not a Plusnet router) you will know the new password to enter in the router. Note that you will only need that if your router disconnects (a new password in the member centre will not force a disconnection).
One way to decide if your router has indeed updated since any member centre change is to see if it has successfully reconnected by comparing its uptime with the time since you suspect you may have changed the member centre password.
