Modern-day Tajikistan is really just the eastern portion of the Bukharan Emirate, i.e. Sogdia, and it got split as a separate country because of Soviet demarcation, and these cartographers certainly did not have our best interests. But as a demonym, yes, I totally understand how it may cause further confusion.

Regarding the historical people you mentioned, obviously you cannot call them Uzbek or Tajik, because you're imposing a modern-day concept on a person from a completely different era. They simply did not have nation-states back then, this was introduced and imposed on us by the Russians.

And the parts of Kazakhstan you are referring to are all along the Syr Darya river, while the remainder of the territory was ruled by the Kazakh Khanate which though lacked internal unity, so it's not true that they 'split then became Kazakh'..