According to the information, Chrome 107 and 108 are globally replacing the Android browser’s native credentials list with the Google Password Manager.
Now, you will get a new badge in Chrome settings and tapping opens the experience powered by Google Play services.
Some users might already have it with version 107, but Chrome 108 looks to widely enable it. As per the new info, the new stable browser release is still rolling out.
Just tap on the Chrome > Settings is much faster than opening the Settings app > Google > Manage your Google Account > Security > Password Manager.