Oil leak?

Clean it off and dust it with some baby powder and then look to see if new oil shows up. If you don't see new oil it's probably burning it. There is a procedure that you normally use to see burning Top the oil up to full. Drive the car 1,000 miles and then check the oil again and top it up and measure the oil that you added. These days many of the companies say that a quart in 1,000 miles is "normal". The problem with that is that oil burning can poison the converter.

Oil pressure senders are a common leaking point. The leak near the starter could be a valve cover leak weeping down that way. The sender is easy to change. Get the new one (GM please, aftermarket ones tend to leak faster) and get the oil pressure sender socket as well as a loaner tool. Then remove the electrical connector, unscrew the old sensor and screw in the new one be careful as it's easy to do damage if you tighten it too far. The spec is 16 ft lb, or just snug.

Grab a can of carb or brake cleaner and hose off the grime and see where it is leaking from. The senders can spray out oil that gets blown around by the airflow under the hood. Other leaks will tend to seep and run down. That is where the powder trick can help as it will show the direction of flow.

Let us know what you find. I suspect you will find it's either the sender or a leak farther up as both are common.