As for "the Steppe", I'm not sure what you mean. There is a whole lot more in Turkestan than Steppe. Bukhara, Khiva, etc., not to mention the Silk Route. There are plenty of reasons for heading in this direction. A Kazan Khanate with some Ottoman help would be a lot for Russia to take on, especially with the Crimeans and Ottomans themselves.
This is the 16th c I'm talking about, not the later period. Azov was totally inconsequential to the Ottomans in OTL - they had no interests in lands East of this. If they had, they would have put more attention into defending it.
I suppose it depends when in the 16th c. you mean, I suppose. And I think you underestimate Ivan's state somewhat.
What do I mean by "the steppes" - well, Ural and Bashkiria and Kuban, largely. You need Astrakhan to hold that.
Of course, the failed Ottoman expedition to Astrakhan happened at a time of overstretch (at war with Austria), but Crimea's successful attack on Moscow also happened when Russia was at war with all their western neighbours put together. I'm not sure what it says about either side except that Russia came back despite the succession crisis and the Ottomans never tried again. It's that logistic tether again.
Khiva/Bukhara/Samarqand - isn't it easier to beat Persia and take control of the traditional Southern Silk Route?
As you said, the Russians (much closer geographically and more experienced in this) had real limitations until the mid-19th c. The Ottomans I imagine would have the same problem. They're not a local nomad power anymore, they're a European empire.
Best-case is when you DO build a Volga-Don, DO capture Astrakhan, and DO manage to keep propping up Crimea and whatever other Khanates they manage to set up to take care of other steppe nations (Probably just the Nogais? Kazan seems just too far away. You might as well be trying to control Krakow. Whereas from Nizhny Novgorod to Kazan is no farther than Constantinople to say, Athens. And Kazan was politcally unstable, and militarily uncertain. You'd have to invest into it as much as into Crimea to prop them up).
Then you could trade along the Caspian through Rasht and down the southern route, AND keep a steppe frontier while trading along the norhtern route through proxies.
But it's easier, in any case, to control Persia instead as a sufficiently resilient Persia makes all that investment vulnerable as much as a sufficiently strong Russia does.
If they completely concentrated on the Russians in the 16th c. I'm sure they could have beaten them and stymied the Volga expansions, but I don't think it would have been worth the price long-term and their loss of interest is probably well-justified.