Many recipes like stuffed peppers call for baking already fully cooked rice for upwards of an hour at ~375 F. I’m surprised the grains come out intact and texturally not that different than before they were baked. Why does the rice come out not tasting overly mushy or over cooked?
Rice does taste a little different after baking, and its texture is also a little different, but the reason it is not mushy or overcooked is that the recipe controls the moisture levels. Totally uncovered it would dry out completely in the oven, and with too much water it would become mushy, but inside something like a stuffed vegetable or sealed pot the extra cooking time doesn't have too much of an effect.
There are several factors involved here.
This plays quite a big role. My mother would usually run out of peppers and place the extra stuffing in the pan alongside the peppers. The texture between the two portions of rice, from inside the pepper and outside, is quite different, even though they were baked together. The main reason should be the reduced water inside the pepper, which doesn't allow the rice to hydrate fully (but you still have to poke a few holes in your peppers or you will end up with completely undercooked rice).
It doesn't start out fully cooked
You don't stuff peppers with completely cooked rice. Rather, a pilaf method is used. The stuffing is prepared by pre-frying the rice in fat, either with the meat and onions or separately. It isn't cooked by that time, only "loaded" with fat. The actual cooking comes in the oven.
You can make stuffed peppers with any rice, but if you try some long-grained rice types such as jasmine, it will end up quite soft - not inedible, but markedly softer than the out-of-the-ricecooker texture many people consider a standard. There are rice cultivars which cook up firmer.
Whenever you try to cook a starchy food in acid, it ends up firmer than without it. A bell pepper does have a bit of acid, like most (botanical) fruit, and recipes frequently call for capping the stuffing hole with a slice of tomato. This changes the pH of the rice inside the pepper slightly.
Ovens can be remarkably slow in getting water to a boiling point. In dishes where you don't stuff the rice, such as baked lamb with rice, you start out with completely raw rice, and it simply takes 1-2 hours to cook the rice to the point it would have cooked in 20 minutes on stovetop. A similar effect applies to stuffed peppers, but there you start with partially prepared, still warm rice, so the hour would overcook the rice if not stuffed.
Oven rice recipes don't make you add your water at the beginning. Rather, you typically start with little water, and adjust it over time - a bit like risotto in slow motion. In the times where the grains have soaked up all available water, they cannot continue towards overcooking until you give them a bit more water. And if you never give them enough total water to get waterlogged, they will never get mushy either, despite experiencing high temperature for a long time.
If I try to be objective, I believe that the rice is many oven-baked recipes is different in texture from the rice coming out of a Chinese rice cooker. It is just that it is considered the "normal" texture in these cases, so nobody calls it "mushy", even though it would be somewhat softer if compared side-to-side.
This case has to do with air flow, as well as moisture from the additional materials.
The pepper in the outside, and the mix that is combined with rice is often raw. Vegetable like the pepper, onions, and other components all impart water or steam to the stuffing as it bakes. Meats contribute water and fat to the mixture. If there is all vegetable and no oil added, you’ll likely get more of a steaming effect than if there is oil incorporated.
The pepper itself is also a container. By stuffing it, you are limiting how much airflow and where the airflow occurs. The stuffing will receive thermal change, but the moister only escapes from the open end. Having everything contained in anything would help in the same why (i.e. put the mixture in a cup and bake it, and the contents will still more moist). Spreading it out on a sheet pan, you increase the surface area, which will increase the rate of evaporation.
As proof of concept, put the cooked rice one some parchment paper, and then wrap it in a loose ball of tinfoil. The foil should simulate the pepper, and the parchment will stop the rice from sticking to the foil. Compare that to rice cook without the foil and you should see the impact that airflow has to evaporation.