With an apron sink you know upfront what the dimensions are for that front edge.

With an undermount sink you need to discuss the width of the front rail with your fabricator. I always tell them I want the narrowest front rail they can fabricate. Don't assume the fabricator shares your same definition of "narrow", so always discuss the details.

Mine is 4". My sink rail is 48" long, so not sure you would want anything narrower over that length. With a smaller sink I might have pushed the fabricator to shave off 1/2 inch more.

Chispa By fabricator, you mean the countertops installer? How does the plumber get involved? Does the plumber set the sink, then the countertops get put in place? Novice here.

"How close will a workstation apron sink be vs. a workstation undermount sink to the user?"

I've gotten undermount rails to be as thin as 2 3/8", but you have to strap a sink in place to do that because there isn't room for clips and because the sink has to help support such a skinny rail. Apron sink rails can be 1" - 3", so that's the most sure-fire way to get as close to the bowl as possible.

"Will it make that much difference (reduce back fatigue, closer center of gravity for safer knife cutting)?"

If undermounted, an apron sink is 3cm lower in the front than an undermounted sink. I've had customers in wheelchairs grateful for the lower sink front and easier access.

"How does the plumber get involved? Does the plumber set the sink, then the countertops get put in place?"

With new work, a carpenter may scribe a sink into the cabinet if it isn't self-facing and mount it just below the cabinets. The sink flange is siliconed, and the top is set on top. The plumber connects the supply, disposal, and drain lines.