say grep { REGEX } @list;
#doesn't work, because it isn't really doing what you think it is doing

say grep { /REGEX/ } @list;
#doesn't work because of the problems mentioned above when using constants in contexts that auto-quote barewords

say grep { /(?^:string)/ } @list;
#this works (and throws errors if // are removed)

use Readonly;
Readonly::Scalar my $regex_ro => qr/string/;
say grep {/$regex_ro/} @list;
#this works (and, as expected, gives same bad result you got if // is removed)

my $regex = qr/string/;
say grep { /$regex/ } @list;
#this works (and, as expected, gives same bad result you got if // is removed)