We've taken our cabrio into a local mechanic first for this light, a couple of times, and then to the dealership now twice. They've changed out the fuel pump relay, MAF, all hoses, oil dipstick funnel. The last time at the dealership is when they changed the hoses, the fuel pump relay, and purged the solonoid (?). They told us that if the light came back on, they'd have to replace the solonoid. There have been numerous codes, and a lot have to do with fuel system components being shorted to ground, and a long term fuel trim too lean. Injector circuits 1-4 shorted to ground, evaporative canister purge valve circuit shorted to ground, secondary air system shorted to ground, evaporative leak detection pump circuit shorted to ground, idle speed adaptation limit reached. My question is, could this solonoid cause these issues, and what solonoid are they referring to?

First, how is the car running? Smooth but with the check engine light on.
Or is it running poorly and perhaps due for some engine maintenance?

Secondly, what are the codes? There may be multiple codes set in the emissions system. You mentioned a solenoid as a potential problem. In the emissions system, that could be either the Evap Purge Solenoid or the Canister Vent Valve Solenoid.
If one of those were replaced because it was sticking intermittently or completely failed, but the light is back on, replace the other solenoid.

Sometimes the diagnosis on these evap systems can be tricky. Especially when the problem is intermittent: "Now the light's off, but it was on yesterday." The best time to bring your car in for diag is when the light is currently ON. If need be, call your shop on the way over and when you get there, don't shut the engine off. Leave it running until the tech can get the scan tool plugged in.