Rain Booties that go over Cleats
Shoe covers/booties will help keep your feet dry, but there's really no such thing as "waterproof" shoe covers/booties.  The best of them merely delay your shoes filling with water for maybe 20 or 30 minutes in any decently heavy rain.

Even if the material itself is waterproof, there are too many ways for water to get in.  First, water is going to run down your legs into your shoes. Shoe covers won't help that much if at all. You can help keep water out of the tops of your shoes by wearing tights or some other clothing that fits over your shoe tops and directs water outside the shoes.  But even that won't keep all the water out. ("Hey, I'll just wear waterproof pants!"  isn't an answer - after a few minutes that can be like cycling in a sauna because waterproof works both ways...)

Water is also going to get in through the soles via the cleat holes, unless you have specially-designed shoes such as "winter cycling boots" that are designed not to have this problem.  Or don't have cleats at all...

And even then, if you don't have fenders with a good mud/spray flap on the front, the spray from the front wheel will rapidly soak your lower extremities anyway.  Spray enough water onto your shins and your shoes will be filled no matter what they're made of and no matter what you do to keep water out of the shoe tops.

So, if you want to keep your feet truly dry, you need to start with fenders with a good mud/spray flap to keep most of the water off your feet and legs in the first place, and leg coverings/tights/pants that direct most of what does get on you away from getting inside your shoe tops.  Then, you need to prevent water from coming up through the sole - and that requires special shoes, or not riding with cleats at all.

Shoe covers/booties are in the "keep your feet from getting totally soaked for just a few more minutes" category.  If that's all you need, that's fine.  But they won't keep your feet dry.  To do that, you need a lot more help.