But is that how a project like Panopticlick calculates "similarity" across bit-vectors?

I've no idea about pana-pano, that thing, but ostensibly, it can be as simple as counting the number of matching bits (properties):

my $needle = getBits();
my $nBits = unpack '%32b*', $needle;

for my $straw ( @haystack ) {
    my $similarity = unpack '%32b*', $straw & needle;
    print "Percentage similarity %f\n", $similarity / $nBits * 100;
}
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For parts/product catalogue type applications, bit-mapped data records can be very effective and efficient, because their attributes tend to have a fixed (and limited) number of values. Ie. Half a dozen colors; half a dozen sizes; 2 or 3 finishes; etc. That means each choice can be represented by a bit position in a vector. Selection can be extremely fast.