I finally had my container shed, but it was super dark inside, even with both doors wide open in the middle of the day. The rust-red paint on the inside seemed to absorb most of the light that gets in.

That had to change. I was not in the mood for rummaging with a flashlight through the back of the container each time I had to get something out. I wanted a lighter and more reflective color on the inside, such as white.
Yet I was not in the mood to paint the inside with a brush or small roller. So I went ahead and invested in a small paint sprayer that I also could use for other projects later.
Using a paint sprayer was a smart move, if I may say so, turning this painting project into a really quick job. And the result delivered exactly what I had hoped for – some more light that would allow me to find things even in the back of the container.

Yes, that color makes it much more usable. Is the container constructed from ferrous metal? in other words, can magnets adhere to the walls? If so, you have more flexibility in arranging the contents. All in all, this project looks very successful and is a good improvement for your property.
Thanks for the posting and stay safe.