For shared-mem/mmap operations...

What you're saying about shared mmap is correct, but I'm not sure why you think this has to do with what's going on here. The strace clearly shows MAP_PRIVATE, and also, why should that string ($x) be shared with other processes (like code of shared libs)?

And, again, mmap is generally only used for shared libraries.

I don't think so (though it depends on how you define "generally").  The three write lines in the log mark: (1) before allocation and (2) after allocation of my $x = " " x 2_000_000;, and (3) after undef $x;. Why would those mmap/munmaps that happen in between those markers be related to loading of shared libs, or some such? Doesn't make much sense to me.

The only thing that remains to be explained (IMO) is why perl mmaps two blocks of 2002944 bytes, but only munmaps one...

(When you do the same with an array, e.g.

    my @x = ();
    $x[1_000_000] = 0;   # mmaps   8003584 bytes
    undef @x;            # munmaps 8003584 bytes
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the required size (to grow the array) is mmapped/munmapped exactly once each.)