Hello. Nice buy! The new S-type is Jaguar XF, that's the new S-type...
Yes, indeed, you have a ZF transmission and it's much more reliable than Ford's 5R55N that had many problems. The engine is Ford's I believe

But it's good, don't worry. I drive 2000 S-type model 3L (Ford Duratec) - the engine is good - it has some ignition coil problems from time to time, but the biggest concern is of course the transmission - problems from the very beginning I bought it (3 years used one).
My main concern is also about suspension - many bushings can't be replaced without changing wishbones... they do cost a lot... As long as you have good roads over there it shouldn't be a big problem.