This is a website preview in the taskbar, but not in the side panel. With all that space it occupies on hover/press they could've added a preview. Also, this design is not in line with any other design Microsoft is currently trying to promote.
Support is still in an experimental stage as certain features are not implemented at this point in time. One of these features, the ability to resize the tabs sidebar, has now been implemented in the latest Edge Canary build.
All you need to do is move the mouse cursor over the sidebar border; the icon changes and you may click and drag to resize the sidebar. You may reduce the size to make up more room for the display of websites, or increase it to make sure all page titles are displayed properly, even in lower levels of the hierarchical structure.