"does Role::Tiny -> apply_roles_to_object() actually create a new anonymous package and is reblessing the object"

That's a feature.

use strict; use warnings; use feature 'say';
use Role::Tiny;
package MyClass { use Moo };
package MyRole { use Moo::Role };
my $o = MyClass->new;
Role::Tiny->apply_roles_to_object($o, 'MyRole');
say ref($o);
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Output:

MyClass__WITH__MyRole
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