I agree it's very annoying that on the callee side, i.e. in the sub, it's virtually impossible to distinguish between being called as a function or as a method.

{
    package Foo;
    use Devel::Caller qw(called_as_method);
    
    sub new { bless {}, shift }
    
    sub foo {
        my $arg = shift;
        if (called_as_method(0)) {
            ref($arg) ? "object method" : "class method";
        } else {
            "subroutine";
        }
    }
}

use Test::More tests => 3;

my $foo = Foo->new;
is( Foo->foo,       "class method" );
is( $foo->foo,      "object method" );
is( Foo::foo($foo), "subroutine" );
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(although wanting to do this in real code is nearly always a sign that you need to rethink your design :-)