You have to have room for the faucet too. If you get a sink that fills up the whole cabinet, you have to shift to the much more expensive wall mount faucet.

No, no, the sink would fit the width, but would be some sort of standard depth, so there would be room for a faucet in the back of it!

My issue is that I cannot find info as to whether the sink's rim/flange can indeed rest on the top of the cabinet's sides (there is room for it, and it would not interfere with the stone countertop). But I cannot find any info!

"1) Can the rim/flange of said sink bowl rest on the tops of the cabinet's sides, between the front and the back rails? (This would support its sides. The front and back would have to be either strapped in, I imagine, or attached with clips)."

You don't want the cabinet sides/blocking to support your sink directly. Cabinet sides cannot push a sink tight to the bottom of your top as a strap system can. I regularly rip cabinet sides and have sink flanges extending past them. When the sink is strapped in place, not clipped, you've replaced the structural support the cabinet side provided with sink.

"2) Do I HAVE to get a sink with a footprint that completely fits inside the cabinet's inside space (22.5"), thus reducing the possible dimensions of the actual bowl considerably?"

No. You can scoop cabinet sides to allow a sink installation, especially if the sink is strapped in place. It depends on what's adjacent. Drawers? Not so much. Fillers? scoop away. Hercules Universal Sink Harness from BB Industries, or a Sink Strap or two from Regent Stone Products please.

Ripped cabinet side top; Sink Straps in place.

Sink flange extends past cabinet side.

Bear in mind that installing an undermount sink by having it rest on top of the cabinets means that if you ever have to or want to replace it you would have to remove the countertops. This is not something you would find fun or inexpensive, to say nothing of potential damage.

I would tap off the cabinet front and rip the cabinet sides before I'd ever remove a non-solid surface countertop in order to change a sink. No danger to the top or cabinets.

Joseph, thank you so much for your answers! So basically I can get a sink with a rim that extends over the cabinet side, and mount it with straps or HUSH for support. I am not limited, and can get the largest sink that can fit in my 22.5" of available space. I am relieved to hear this, because the 18" bowl the contractor wanted to give me seemed way too small... just a step up from a bar sink, in my view.

Replacing the sink in this case is a very remote possibility. It's a rental unit, and I will get a 16 gauge sink or so, so it should be sturdy enough.