Well the suicide theory is connected to his lifestyle. The story is that he was blackmailed into killing himself or his affair with a government official would be revealed (causing him possible exile and his family embarrassment). What’s sad is that he certainly would not have been exiled. The Tsar would have thrown the accusation in the garbage like he did with such accusations about notables all the time.
One need only look at the crop of great musicians from Russia who evolved about the time Tchaikovsky made his debut on the world state and the dearth of them after the Bolshevik Revolution. Those who survived the Communists either escaped or somehow managed to convince the Bolsheviks they were promoting their new world order.