Can the sidewise window be made to dock inside the chrome window?
Unfortunately, limitations in the Chrome API prevent this.
Sidebar support was initially considered a few years ago, but rejected. The issue is supposed to be reconsidered by the design team this year. Since the main problem this solved was the "bookmarks sidebar" one, the future of "Sidewise docking" is uncertain; more focus will probably be given to bookmarks than sidetabs.
EDIT: Here's Joel's comment on this issue:
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