Turkey does have some recent history of "balancing" with Russia, but I'm not convinced its decisions on the Straits are an example of that. My understanding is that under the Montreux Convention, Turkey closes it for everybody involved in the war or nobody, I don't believe it allows Turkey to block one side of a conflict's ships but not the other, unless it is a conflict in which Turkey itself is directly involved. (In a direct war between Russia and NATO, Turkey would probably just tear up the Convention anyway–but doing so in peacetime would likely be considered by Russia to be an act of war.)

In practice, however, closing the Straits has a much more negative impact on Russia than NATO, since the major NATO naval powers (US, UK, France) were never likely to send ships near Ukraine anyway, and as non-Black Sea states the Montreux Convention subjects them to special limits to which Black Sea states are not subject. In fact (according to some sources), the Straits are still officially open for the US/UK/French/etc navies, so long as they don't directly join the conflict – although I imagine they'd be rather hesitant to exercise that right at the moment, due to the risk Russia might interpret such an act as hostile.

If it is true they allowed some Russian ships through before closing it–that could have been simply the slowness of government decision making, plus the legal complexities involved, rather than a deliberate "balancing" act.

If anything, I think this conflict has caused Turkey to turn away from the "balancing" and move more firmly into the NATO column. Reminding NATO of their value helps silence the ongoing "can we expel Turkey?" debate, refusing to do so would have given it more steam. Turkey has been selling its TB2 drones to Ukraine, which Ukraine has been using to great effect against Russia – not a very good example of "balancing". Ukraine's successful use of Turkish drones is very helpful to Turkey, because it gives them more information on how they perform in an actual conflict (which they already had to some extent with the Syrian civil war, the KPP, etc, but Russia is a very different kind of adversary from the Syrian government or the Kurds), and also helps attract potential buyers.