Where did the thin, smooth plastic spatulas go?
The old thin utensils were made of Nylon.

The reasons they are hard to find is that traditional Nylon is difficult to manufacture within food standard guidelines for PAA (Primary Aromatic Amines) migration, and does not bio-degrade or burn safely. For relevant references, your local government health department will have papers on PAA migration.

Given that, many utensil manufactures have moved on to other plastics, mostly silicone. Though some use PA66 (Nylon 6,6), which is that thick chunky black plastic stuff.

Try wooden spatulas. They are simple, clean, disposable, and you can get them in thin wedge shapes (e.g. at Asian supply shops).