I'm 99% sure they will fit as I've had both the older Weber Genesis and newer Weber Spirit 3 burner and the grates are interchangeable. And as I understand it, the Weber Spirit and Spirit II lines have the same grates.
That being said, you can get way cheaper parts if you're willing to go 3rd party. For example, the following grates are almost 1/2 the price. And note that they say they fit the old Genesis, Spirit, and Spirit II 3xx lines so in case you decided to look for another set, you can look for something that fits any of those lines.
https://www.amazon.com/Uniflasy-Inches-Cooking-Genesis-Platinum/dp/B0822B667P
The OEM grates that you listed are not solid rods. They are flat sheets that are bent in a U shape. The ones I listed above are solid rods so they should be more durable. BTW, I'm not saying get that exact set. It's just an example of the price difference. Also, if you want the bent metal, that's fine too. They will probably heat up faster than solid rods.
My recommendation for replacement grates are actually GrillGrate. They are extruded aluminum and I use them flat side up. They do an incredible job. The only issue with them are that they are very non-traditional, are a bit more expensive, and some people don't like the idea of cooking on aluminum.
https://www.grillgrate.com/products/replacement-grillgrate-set-for-weber-spirit-300-series/
This guy agrees. BTW, in case you haven't heard of this site, it's considered one of the more respected grill related sites out there. This article goes over what type of grates are best.