I would seal the concrete as a first step. Something impermeable like epoxy or an oil-based paint. Years ago I planned on putting tools in my pole barn with a concrete floor, but the moisture wicking up and evaporating kept it way too moist for shop tools.

I recommend vents.

FWIW, rust on unused tools is common.

Sealing the concrete sounds like a good idea, but it's not feasible this year. I'd have to (1) order sealer and wait for delivery, (2) move everything out of the shed, probably about two days of work, (3) apply, and (4) move everything back in. I'd have to do all of that before the rains begin -- in three days, if the current forecasts are correct -- while working a full-time job and helping my wife with another project that has to be finished before it gets wet.

Other construction projects like installing vents would suffer the same difficulty. I have a working air conditioner in the shed, and I have an electronic timer; that will have to do for now. If it only makes the room a little dryer, that's an improvement over nothing at all.

By the way, my experience with unused tools has been different. I have never seen them rust unless they were stored in excessively damp conditions.

We'll see whether some air circulation helps. I've decided to try two hours a day, 7-8 AM and 4-5 PM.

I think you're overengineering the approach to a solution.

If you have excess humidity, and electricity, why not simply install a dehumidifier? Don't provide more ventilation to the outside, it will only make the situation worse with whatever you use.

There are a number of ways to manage humidity - increased air flow, removing the moisture from the air, and a third way I know of .....

I live in the SF Bay Area. When I had a sailboat, there was a year-round problem of managing the cabin dampness to avoid mildew and other problems. We put in a small marine heater - I think it was something like 300 watts or less and looked like a 3-4 foot long aluminum pole. Very safe and it kept the temperature of the cabin in the 50s. So a third way - is to increase the temperature of the space, that decreases the relative humidity.

I call that overengineering. A basic dehumidifier costs about $175 (I just checked Amazon) and draws 250 to 300 watts. It also requires me to open the shed regularly to dispose of the collected water. That's an extra task, because in wet weather I don't do shed things, and I often don't go in there from one week to the next. The air conditioner is free, since it's already installed, its fan can't draw anywhere near as much power, and it doesn't require attention.