My 2002 Saab 9-5 turbo started smoking. There is oil going into the throttlebody. Is this a failed turbo or something else?

It appears to be a known issue.
Blue smoke is oil.
White smoke is water.
Black smoke is rich mixture.

Blue smoke is probably from the turbo bearings.

https://www.google.com/search?q=saab+9-5+P0303

Vacuum Hoses

https://www.google.com/search?q=2011+Saab+9-5+Turbo+4.+vacuum+hose+diagram

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check the oil level. Probably not enough oil in the sump because the oil seals in the turbo have failed and the sump oil is going out the exhaust system

Sounds like the turbo. Have you ever changed the turbo? If not, I would bet on that. If you've changed it but have more than 60-80k miles on it, same.

It more sounds like a broken or faulty pistons ring/s, if so it's cheaper to have another engine on that car.

WHITE SMOKE MEANS ENGINE IS BURNING ANTIFREEZE.TURBO WILL SMOKE HEAVY BLUE WHEN TURBO SEAL FAIL.ALSO YOU WILL LOSE POWER.YOUR CAR IS TOO NEW.TO HAVE PROBLEMS.YOUR CAR SHOULD BE WARRANTY COVER.TAKE IT TO SAAB DEALERSHIP.LET THEM CHECK IT OUT.

Depending on the overall condition of the engine, it could have worn or frozen rings, worn valve guides or the turbo you installed is worn out. These are driven by exhaust pressure and if their bearings are worn, you may be getting a mix of compressed air from the turbo and oil that is seeping past the compressor's internal seals.

The valve stem oil seals require replacement.
This repair can usually be performed without removing the head from the engine, so it should not cost too much.

side of engine by firewall passenger side 1/2 way up bock with single wire going to it

One way to check for a blown head gasket, is to simply smell the coolant reservoir. Pop the cap, and see if it smells like raw gas. Every headgasket, I've diagnosed has had this smell, even if the oil is not contaminated. Another way is to hook up a coolant pressure tester, and run the vehicle for 15-20 mins or so. If the head gasket is blown, the pressure will exceed 15 psi. sometimes as high as 25 psi. If there is oil in the coolant overflow tank, the head is cracked, about 90% of the time.
I'm working on a 03 Saab 95 2.3l t. This vehicle smokes on initial start up, then the smoke disapates, and the vehicle is fine. Another mechanic diagnosed it as bad valve seals. I disconnected the pcv system, and the vehicle no longer smokes. If the valve seals have gone bad, the vehicle will smoke on acceleration. Also if the turbo seals are leaking it will smoke more heavily on acceleration.

White smoke from exhaust = water into the cylinders, when this happens it usually means head gasket gone or starting to go.
Check the water level, and take the car to the garage for a check up , if it is the head gasket, as I think, you risk to blow the engine at any time.