It is not unusual to get 200,000 or more miles from a 3.3 or 3.8. It's
an old style single camshaft with pushrods design.

Early 3.3's had a problem of rocker arm towers cracking at 150,000 or
more miles, but I believe that was fixed before 1996.

Other than that, it would be the usual stuff, such as piston rings,
rod and crank bearings, and valves. The timing chain could be
stretched after that many miles too. A visual inspection would be the
only way to know for sure.

Does it use any oil? Are there any noises that would indicate any worn
parts?

-KM

As long as its well cared for, there's no fundamental reason that it
won't last another 100k miles, maybe 200k. Maybe 300k. The 3.8 has a
chain timing drive, and there's nothing that will likely fail suddenly.
Most likely, the bearings will slowly wear until it starts showing low
oil pressure at idle, or oil consumption may creep up as the rings wear.
Even then, rolling-in new bearing shells would keep it going a lot longer.

If you define failure as a broken connecting rod or broken crankshaft,
you might say nobody knows when failure occurs.
With high miles you usually see leaking oil seals, oil burning, noisy
valves and loss of compression and power due to bad valves or worn rings.
Lots of things could have you call a tow truck.  Dead fuel pump is a
common problem.  Your alternator can go at an inconvenient time.  You
already had problems with the trans.