This is the old sink faucet with shower diverter.
I replaced it with a $9 (plastic) faucet assembly from Home Depot. It doesn't contain a diverter valve for the shower.
Instead, I created a new shower valve assembly and tee'd it into the water lines below the sink. I removed the threaded fitting for the flexible hose from the old faucet assembly and adapted it into my new valve arrangement.
This is what it looks like from the backside. It's custom made from valve parts, copper pipe fittings, etc.
This is the whole thing.