First off, Welcome Aboard. Congrats on your new WE-4.
All '86-'87 Turbo Buicks rolled off the assembly line with a Garrett TBO-348 turbocharger. (The GNX's received a custom ceramic turbine wheel equipped Garrett turbo)
One quick way to tell, on the inlet side of the turbo, where the air inlet hose/pipe connects, does the turbo have a 2-bolt inlet bell?
And if so, is it a rough finish cast aluminum bell with a port built into it with a rubber hose plug or pipe connecting to the passengers side valve cover? Or is it a smooth finish Billet aluminum inlet bell?
Cast finish inlet bell with breather port is a factory style inlet bell. And chances are, it could be a stock turbo.
Here are two pictures of a stock turbo.
99% of all aftermarket turbos for Buicks, starting back in the early 90's had a billet aluminum 2-bolt inlet bell. I know the first upgrade turbo I ever saw for a Buick, was an old Stage 2 turbo from ATR back in '91. It had a billet aluminum inlet bell. If the turbo looks like these pictures below, chances are it's an upgraded turbo.
The TA series of upgrade turbos, utilized the factory TA series compressor cover that was machined to match the contour of the compressor wheel. (TA-49, 60, 51, 52, 53, 54, 61, 63, 66) Circa '91 - current.
If the compressor cover does not have a bolt on inlet bell, but rather a molded in style inlet, it would definitely be an after market turbo.
Pics would be great, but if not, you could take some measurements of the compressor wheel by taking off the compressor cover and we can better help ID the turbo.
Hope this helps a little and welcome to the world of Turbo Buicks.
Patrick