You also fall prey to using a my() variable in the same line that you declared it:

use strict;
use warnings;  # DON'T turn off the uninit warning

my $x = qr/(a(??{$x})?b)/;
print "x1($1)\n" if "alphabet" =~ $x;
print "x2($1)\n" if "caaabbbc" =~ $x;

my $y;
$y = qr/(a(??{$y})?b)/;
print "y1($1)\n" if "alphabet" =~ $y;
print "y2($1)\n" if "caaabbbc" =~ $y;
__END__
output:
Use of uninitialized value in pattern match (m//) at rx line 2.
x1(ab)
x2(ab)
y1(ab)
y2(aaabbb)
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See? The $x regex is looking for $main::x (although it doesn't give you a strict-breakage, since it's not looking for package names in the code that handles (??{ })), and it's empty, so you get a warning.

Take out the \A anchor, but also declare the variable first and then assign to it.