Firstly use constant doesn't define its constants with the sub name in the correct package. Moo::Role knows they were compiled into the constant:: package, not into your role, so doesn't copy them to your class.

Secondly, with is operating at run-time, not compile time.

You can solve these by using PerlX::Define to define your constants, and wrapping with with BEGIN { ... }.

use v5.16;

package MyRole {
    use Moo::Role;
    use PerlX::Define;
    define BLAH = 42;
}

package MyClass {
    use Moo;
    BEGIN { with 'MyRole' };
    sub do_stuff { return BLAH }
}

say MyClass->new->do_stuff;
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Or (same idea) just manually do the constant sub yourself:

use v5.16;

package MyRole {
    use Moo::Role;
    sub BLAH () { 42 }
}

package MyClass {
    use Moo;
    BEGIN { with 'MyRole' };
    sub do_stuff { return BLAH }
}

say MyClass->new->do_stuff;
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