One of my favourite things about Core SSH was the side-tab arrangement. I just find it a million times easier to read tabs in a vertical list rather than across the top where they keep getting truncated and shortened.
I would really love to have an option to use side-tabs in Core Shell. You're basically this one feature away from making my perfect SSH client 
I think the trouble is that it is difficult for you to distinguish shell sessions from different hosts. But it has other solutions, such as tint the tab icon according to their foreground/background colors, which is already in our dev pipeline.
Top tabs are fine for 3 or 4, but not for 5 or 6 or more, and I often have that many tabs.
I understand, side-pane and top-tab each has its advantages and disadvantages. Side-pane could lose multiple windows support, while top-tab is difficult to distinguish if you have a dozen of tabs.
We can't have both by simply providing an option switch between them, add side-pane means the whole UI must be redesigned thoroughly.
As I mentioned in last comment, tint the tab icon according to their foreground/background colors can help us identify different shell sessions easier, and may add more built-in icons in future. After all, a picture is worth a thousand words.