I would think the carbide would only be necessary if what you were trying to cut was really hard, like approaching the hardness of ceramic tile. A stainless steel sink should still be relatively soft, after all they form it by pressing/drawing it and you can dent it during use. A toothed bi-metal holesaw should cut it. Use a bi-metal saw because the blade will be harder than the cheaper one-piece blades. Hole saws typically use an arbor that chucks into a drill, the arbor also having a center pilot drill to hold the saw in position and to start the cut. You should cut from the back side to avoid damaging the good surface. You might also clamp a block of wood (USE SOFT JAW CLAMPS!!!) to the back side (good side of the sink) where you are drilling to give the drill/saw something to bite into as it comes through the thin metal. Run the saw at a relatively slow speed unless you are familiar with using a hole saw as they can sometimes grab and jump or get away from you. The concern here is if they grab they might warp the edge of the SS hole - not a huge issue as most plumbing trim rings cover a rather wide area.

I needed to expand a hole in a cast iron sink..probably much more difficult than stainlees steel. Now that was a head scratcher. After much scratching I used Dremmel tool with a mini-grinder and expanded the hole from 3/8 to 3/4. This took about 15 minutes but it worked. I would think that you could drill a pilot hole then expand it the same way only quicker. I dont know how the metal will react so you might want to experiment first

Disagree with all above.

Go to rental store and rent (really cheap) a hole-shearing device designed specifically for this purpose. They come in whatever hole-size you may need. What you'll do is drill a hole in the SS big enough for the device's bolt to go through. Assemble the die/cutter of the device on either side of the SS and pull together using the nut/bolt supplied with the device. Clean cut. No heat. No vibrations. No risk of galling or scratching. Takes minutes.

"hole-shearing device"

General name is chassis punch.
Smaller sizes are often operated by a bolt and nut, larger ones are hydraulic.
It will punch a clean hole.
You do have to drill a starter hole to connect the two sides of the punch, often 1/4 on smaller punches, up to 3/8 or even 1/2 inch on larger ones.

Thanks, I've seen those tools. Sounds like the way to do it.

The style bits as in the link also would work well if available in the size you need. I know nothing about the company in the link nor their specific products. It was a convenient picture.

Here is a link that might be useful: An example