It is far far far far far way from replacing TreeStyle, as it has no Tree.... It just moves the tabs from horizontal to vertical, which has similar usability problems

It is better than Sidewise on chrome though, however TabCenter is XUL as well I believe, there are no APIS currently for it to be moved to Extensions,

rubbish, will also be incompatible after this change. https://github.com/bwinton/TabCenter/issues/868

Furthermore, "showing tabs on the side" is not "similar to Tree Style Tabs"

To be fair, "showing tabs on the side" is still leaps and bounds better than "yet another browser that squeezes them into the top, end to end, like a god damn maniac". :)

But yes, the "tree" part of Tree Style Tabs is essential, too.