The Soviet Union certainly did famously assassinate several defectors, in ways that pointed unambiguously to the fact that they were political assassinations. The most famous of these was the assassination of Georgi Markov in London with a "trick" umbrella that shot a pellet of ricin poison into him. The contrivance of the whole thing was clearly meant to scream, "this is a state killing, so if you're a dissident or thinking about being one — WATCH OUT." (Compare that to, say, him getting killed in an apparent robbery or him just appearing to die in his sleep or other things that the KGB could certainly arrange.)

(Solzhenitsyn has an excellent chapter in Gulag Archipelago on the psychology of "The Arrest." He argues that for the KGB agent, making these kinds of things unusually "over-the-top" serves a psychological function for the agents and agency far more than it makes practical sense — it makes them look "busy" and also increases the aura of fear and awe that surround them. It's an interesting theory though Solzhenitsyn was of course not a KGB agent, so one should take it with a grain of salt. But these kinds of killings are certainly performative.)

It breaks the 20 year rule to answer the "do they still do it" question but there are many indications that the answer is "yes." Famously in 2006, the former FSB officer Alexander Litvinenko was killed (again in London) through poisoning with polonium-210, an extremely radioactive element that is not at all easy to come by — again, clearly seen a "signal" that "this killing was done by a state." As recently as March 2018, another former military officer and known double-agent, Sergei Skripal, and his daughter, were both poisoned (they survived) in in the UK with a rare nerve agent that was known to have been manufactured in the Soviet Union.

In all of these cases, three common threads emerge. One, the killings are by methods so contrived and obscure that they are plainly assassinations of some sort, ordered by someone with access to the kinds of poisons that only a state likely would have access to. Second, the killings have just enough plausible deniability in them that while the #1 suspect is obviously the USSR/Russia, it is also hard enough to prove state culpability that they can deny it. The denials are obviously pretty flimsy. Third, none of them took place in the USA... one wonders if they have some kind of "rule" about that or not. I have no idea, but it might be seen as a "step too far," something that might encourage unpleasant repercussions. (But I've got to say: if I were a Russian ex-KGB dissident, I wouldn't move to London!!)

There have at times been efforts to sanction Russia for these kinds of assassinations and assassination attempts. As for whether they are officially sanctioned... one would presume that if it were rogues, they wouldn't continue. You can't get access to polonium and nerve gas without some kind of official sanction; they are not "off the shelf" agents, they are tricky (polonium is very short-lived, so you need a relatively fresh source).

I don't know whether modern-day Russian FSB would hold a grudge against someone who was a defector to the KGB. But the organizations are not so dissimilar and the people are largely the same. If I were Odievsky I would probably not want to chance it. But there is ample historical evidence of the USSR using these methods, and lots of present-day evidence to suggest this still occurs.