If I'm not mistaken, Carullus is more familiar with AE, so I can understand why 'traybake' might not mean anything. It doesn't mean much to me either.
If it's a cookie (BE biscuit) that's baked in a shallow tray or pan, that is, relatively firm and dense, only about 1-2 cm thick, then we call those kinds of cookies 'bars,' because you cut them into rectangular (or square) bar shapes to serve. Chocolate bar cookies are brownies, but we do very often have lemon bars, so I suppose one could also have apple bars.
If it's something with a pie-like dough (rolled out with a rolling pin) on the bottom and apple filling on top, then yes, it might be like apple pie. Though pie is always made in a round pie pan or plate, not a tray.
If the slices are beautifully arranged on some kind of custard-like filling on a French-style pastry crust, you could call it something like an apple tarte. But those too are almost always round.
If it has a top crumbly crust but not a bottom, and a sweet, runny fruit filling with fruit chunks or slices, it could be apple cobbler.
If it's just a cake-style batter that you make in a rectangular cake pan (6-8 cm deep, as opposed to a tray, only 2-3 cm deep) instead of a round one, and the result is the same light, airy consistency as a (birthday) cake, then it would be a sheet cake. In which case you wouldn't use the word 'sheet' on a menu, just apple cake. (Even though that's not a typical kind of cake, because fruit pieces are usually too heavy to use in cake.)
Sorry to introduce more confusion, but it might help to clarify the parameters for either Schnittchen or 'traybake.'