Why does the block use $^a in one place (the automatic parameter) and $a in another place? Shouldn't that be a different (undeclared) variable? (Likewise for b).

No, the ^ twigil is only necessary in the first occurrence. That was introduced because things like this:

my $block = {
      my $v = %hash{$^key};
      say "The lookup {%hash{$^key}} yields $v";
};
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Would complain about the closure inside the string getting no argument, because $^key was interpreted as a formal parameter to the inner-most closure, which in this case was the one inside the string.

Or more general, you couldn't refer to outer lexicals that happened to be self-declaring formal parameters.

So it was decided that after $^foo occurred once, you could refer to it as $foo to, disambiguating it in inner blocks.