How much sag is normal for a plywood shelf on a rolling cart?

That little dip is just plywood doing what plywood does. Half inch stock over a 30 inch unsupported span will always show some deflection, especally once you've got drawers and a supply sitting on it. It's not creeping sag either, meaning it isn't going to keep getting worse over the years, since the wood deflects as soon as the load goes on and mostly stays there. What it won't handle well is more weight added down the road, so a bit of extra stiffness is a good call regardless.

Your instinct about the hardwood strip is right, and it's the cheapest fix. Glue it under the front edge with the strip standing on edge, not laid flat. Depth matters way more than thickness for stiffness, so even a 1 by 2 glued on edge will beat a wider board laid flat. A bead of wood glue plus a few screws driven up into it while it cures, and you're done. Screws alone woud even do in a pinch, but glue makes the shelf and the strip act as one piece, which is where the real stiffness comes from. You don't need to swap the shelf out. If you wanted maximum stiffness you could go thicker stock, but that's overkill for a rolling cart. Another option if the strip bothers you visually is a deeper front rail, basially a 1x3 on edge under the front edge, which doubles as a stop so the drawers can't slide off when you're yanking the cart in and out fast. I did something like that on mine and it's been flat for years. One thing to check before you glue: make sure the strip is crowned up slightly, meaning any bow in it faces toward the shelf. When you clamp it flat against the plywood and glue it, it ends up dead straight and pulls the shelf flat with it.

I agree that the hardwood strip is the quickest fix. Before you go gluing, check how the shelf attaches to the main cart frame. If the side panels are weak or just held by screws, the middle won't stay flat even with a stiffener. When I built my setup, I used angle brackets inside the side supports to firmly pin the shelf. That prevented any sideways wiggle or flex at all. It was a small reinforcement that made the whole unit feel way more stable.

I've seen this happen plenty of times when people try to make furniture out of just raw plywood. While the hardwood strip is a good idea, you really need to anchor it from the inside, not just rely on the glue. If you just glue it on the outside, it'll shift when the cart hits a bump, and you lose all the stiffness. I used 1x2 oak pieces screwed into the plywood from the underside of the shelf, going down through the sides, to really bite the thing into place. Even better is to use some older biscuits or dominoes if you want a cleaner look. They help the joint stay tight, which is always more reliable than just expecting the glue to hold forever after years of vibration and weight from your components.

I think you might be noticing some slight twisting because of how the shelf is connected to the side frame. When I built a heavy equipment cart, I ran into this issue too, and the thing that made the difference for me was using T-nuts to secure the shelf to the vertical supports. That small metal piece locked the whole thing in place. It completly eliminated any sideways wobble or movement at the mounting point, which takes the pressure off the plywood structure itself.

I was thinking about how the weight is spread out right now. It seems like I always put the biggest, heaviest tools on the front side of my storage things. If I move all the big metal stuff and the heavy bins to the very front edge of the shelf instead of spreading it out across the middle, does that help stop the wood from dipping? I guess it just feels right to put the weight at the front, but will that acutally make a difference for a shelf like this?