An update on my repair: Even though replacing the sensor fixed the idling issue, my starter died a few weeks later. Once i started digging through that area of the engine, I noticed some oil pooled at the top of the engine (and, my car was leaking a little bit of oil over the years, but i didn't pay attention to it).
It turned out that vacuum pump gasket was failing, sending one drop of oil at a time down the engine, every few days. It looks like both the starter, and the crank position sensor are both below the vacuum pump! So potentially, the leaking gasket caused the crank position sensor to start malfunctioning, and for the starter to die. Keep an eye on any oil leaks in that area of the engine, and replace the gasket if you notice any leaking oil.
You can pick the gasket up for $40 on amazon, and its a very doable DIY, even for a novice like myself. Just follow the instructions online (note- articles online say that for automatic transmission, you have to move the transmission to get to the vacuum pump. However, there are a few videos online that show you how to replace the gasket, WITHOUT moving the tranny. I've done it. So can you). Once the vacuum pump gasket, and the starter were replaced, the car has been running like a champ.
We talk about Vacuum Pumps leaking on 2.5L 5 cylinder VW engines. This can be a common issue that requires replacing the whole vacuum pump.
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In short, if your car leaks oil from that area, replace the vacuum pump gasket before you get stranded with a broken starter (or your car starts dying at red lights). Fortunately for me, the starter died while i was parked at home.