$functions{$var1} returned undef because none of the regexp keys matched, so $functions{$var1}->($var2) gives that error. The fix is to check whether a key was found in the hash:

my $handler = $functions{$var1};
if (not defined $handler) {
   ...
}

my $result = $handler->($var2);
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Perhaps it's because you never assigned a value to $var1?