We can surmise his intentions from his statements
& actions. This is necessary in order to design the
best response.
But then it also would require attempting to look at the world through his eyes.
Like other former Soviet satellites, Ukraine has been a separate
country since 1991 (USSR's dissolution). The several decades
of independence contrast with the Confederacy's immediacy
of secession. And USA didn't dissolve, unlike USSR.
I agree that the situations are not comparable, but if we're basing our conclusions on his statements and actions, then this may be analogous to how he sees the current situation. It's not just something he's using as an excuse to grab territory just for the heck of it. I think he must really believe it.
To find Putin's motives in what predecessors wanted over
half a millennium ago seems quite a stretch. And with
Turkey being a NATO nuclear weapon sharing country,
it would be a target likely off limits, even to Putin.
It may be a stretch, although it seems doubtful that he would try to grab former Soviet satellites just because they happened to be former Soviet satellites. Besides, the only ones which are left after Ukraine are currently NATO members (except Moldova), so the same argument applies either way.
Putin seems a very strong supporter of the Russian Orthodox Church, and the fall of the Byzantine Empire has apparently been a sore subject with the Russians for centuries. That sentiment subsided somewhat during the 20th century, but Russia and Turkey have had a lot of wars with each other, including the Crimean War which involved France and Britain. Relations between Russia and Turkey have improved somewhat in recent times, although access to the Bosporus and Dardanelles has always been a vital concern to Russia, for obvious reasons.