Happened to me. Going through the steps to reset wasn't difficult. No real downtime of any functionality if you just follow the steps as soon as you get the notification from Apple.
I will also add that yesterday, I received a phone call FROM MY OWN TELEPHONE NUMBER. As anyone can guess, it was a scam message. This one claimed to be from AT&T saying my account was locked. Because it was from my own telephone number, I answered it for a laugh. It's possible the two are related, but I have no idea.
This happened to me. I followed the directions but I wasn't happy about it? seems fishy...This is my suggestion to all....Go into a new browser session and change your password a second time.... Use 2-factor authentication and select the "log out of any existing sessions" so you start clean