Like you, my first bike was hybrid. And my first road bike was an entry-level model, similarly equipped as your Schwinn, although mine was a used fixer-upper.

When I rode that road bike for the first time, my reaction from the very first pedal stroke was "Whoa! I like this." When you pedal Things Happen! The hybrid, by comparison, felt like it was chock-full of the "inert" portion of inertia.

I now have four road bikes, and still ride that first one at least once a week.

Good luck with yours!

Oh, all companies skimp on pedals because the expectation is you'll be replacing them with the clipless of your choice. Higher-end bikes don't even bother with including them.