If you are talking about the cabinet panels they are usually 3/4 Inch wide. If you are building a surround for a full size refrigerator you will need the 30 inch deep panel. For counter depth frig order the 24 Inch deep panel.

Standard refrigerators are 36 wide. So with 2 panels on each side and the refrigerator you will need 37 1/2 inch of space for a built in frig look minimum. Your cabinet installer should be able to figure the install out for you. But you do have to plan and order the materials needed.

If it is next to the wall on either side you will want to allow for 3 - 4 inch spacer to allow for it to open enough to use it properly.

Full depth frig built in look

[Traditional Kitchen design[(https://www.houzz.com/photos/traditional-kitchen-ideas-phbr1-bp~t_709~s_2107) by San Francisco Architect Boor Bridges Architecture

COUNTER DEPTH REFRIGERATOR BUILT IN LOOK

[Contemporary Kitchen design[(https://www.houzz.com/photos/contemporary-kitchen-ideas-phbr1-bp~t_709~s_2103) by San Francisco Architect John Lum Architecture, Inc. AIA

deedles

I would find the specs from the fridge manufacturer and work outwards. Often you can get a pdf of the true dimensions.
If someone is designing your kitchen they should have the autocad file and be able to tell you with absolute certainty.

What I'm trying to figure is the face of the 3/4" panel. The edge, I guess is what I mean. Can that just be covered with veneer and then finished or does it need to be finished with a wider board like a face frame? That first pic you posted, RT... it looks like the front edge of the surround walls are just the 3/4" edge, right?

Sorry
A typical 3/4 edge will get edgebanded or get a thin face frame.
The edge is glued to the panel. Its oversized. Then its flushed to the exact width of the plywood, sanded and finished.

I think it can be done many different ways space allowing. I have seen it with just the 3/4 inch panel and also with a 2 inch filler strip attached to the front edge extending past the panel on either side slightly, that gives it a bulkier look and more built in.

This is the built in look fridge my friend just had done in her kitchen. A 2 inch filler/spacer was put on the front of the 30 inch panel to "beef it up". On the wall side they have a 3 inch filler strip. Her cabinets are full overlay and the spacer does make it look like they are partial overlay. I guess the trade off for a built in look with out custom cabinetry. She also has a piece of filler under the cabinet to fill the gap above the refrigerator so when she buys anew refrigerator she can have the filler trimmed if necessary for the new refrigerator.