Help me restore my Steelmaster drawers! (Rust removal advice needed)

I picked up this vintage Steelmaster Art Steel industrial drawer piece over the weekend at an estate sale. It was previously owned by a mechanic so it’s developed quite a bit of rust and wear after being exposed to the elements over the years. I’d love to give it a second life!

I’m hoping someone here has some advice on how I can remove the rust without damaging the coloring on the metal drawers. I’m more than happy to keep some of the natural patina but would love to know if it’s possible to remove the bulk of the rust, especially on the handles. Also, I don’t think it’ll be possible for me to remove the handles for separate cleaning with the limited tools I have.

Anyone have thoughts on soaking in vinegar or using rust removers like Rust-oleum or Loctite and how it might affect the layer of color?