and main scope itself is also a package just like any other package. Will that help to make ++ overloadable in main?

sure, if you see it that way... you just have to bless your variable, just like you did with your Number-package.

use overload ...;
my $n = bless {number => 23}, "main";
print $n >> 2;
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i think that's not what you want, just wanted to make clear that it's not a problem of the package name but that you must have a blessed object.