I am trying the new Edge Beta version and the Pin to Taskbar is not like other apps on Windows. After pinning edge beta to taskbar, if we open a new window its showing up as two different windows on the taskbar instead of stacking them under one single icon on taskbar.
Attaching the screenshot for reference.
Note: however at any point, it only shows up two different icons on task bar for edge beta for the fact that it is stacking up the new windows that are launched after the first instance under the second icon.
I ran into this as well. If I pin the default Icon it creates a new one with my Profile on it when I launch it. Like you, I needed to pin the opened icon with my profile on it. This is understandable, but not very intuitive for the user. @HotCakeX