If I put my OO class, called Foo::Bar in the examples below, in the same file at the end, Perl does not let me reference the globally-scoped package namespace variable $Foo::Bar::data within methods of this class. However, if I use the same package code and require or use it from an external library, it seems the non-subroutine (ie: method/constructor/etc) code in the class is run.

You need to review what strict vars does for you , see Tutorials

perl is permissive, perl allows you to do pretty much anything , unless you tell it to, hey, protect me from these common mistakes

Coping with Scoping and Modern Perl give a good introduction

I've learned that I can work-around this by using a forward-declaration with our(), combined with a BEGIN block to initialize the package globals. This seems to have the desired result, although I'm wondering if this is really the best way to support using an OO package like this from either a package definition in the same file as main:: or a real module file included with require.

There is a right way to inline a module, see zentara package/module tutorial

our is not a "workaround", when you enable strict vars, our is one way to communicate to strict, this is not a typo, this is a variable of mine

To inline a module you need BEGIN{} because use is executed like BEGIN at compile time

See Coping with Scoping

I'm curious if this is an intentional design limitation of Perl, or merely a side-effect of putting my main:: package code before the Foo::Bar package code. I understand that a require() call will execute the non-subroutine code in the package at that point, but this seems to be in contradiction to how subroutines work; I can call sub_foo() before declaring it, but apparently can't do this with in-file packages.

Neither. Everything including perl has a compilation order and execution order -- this is not a design limitation -- you gotta bake the bread before you can eat it, assemble the bicycle before you can ride...

You can't access the value of a variable before it is assigned, without a BEGIN{} our $data runs after   $foobar_o->text(1); is called ... too late

See BeginCheckInitEndUnitcheck.pl

# Package

Why do you need a comment to tell you that "package Foo::Bar;" is a package? Think about it:)