I don't do much have oatmeal recipes as I have tons of recipes that can have any kind of grain used in them and sometimes I use steel cut oats.
I just used steel cut oats in place of rice for a broccoli, tomato, pesto, feta bake. So yeah, I make a lot of savoury dishes with steel cut oats.
On the rare occasions I have them for breakfast, I add banana, maple syrup, and plain yogurt.
Have you noticed anything where oats specifically don't work well as a substitute for rice? I'd like to use less rice and more oats if possible - or to be more precise I'd like to make recipes with rice that I don't make because I don't want to eat too much rice.
It's more of a personal taste thing, so just trial and error.
It works well for casseroles and bakes that have more of a soft, risotto-ish texture. I obviously wouldn't use it in a dish where I need rice to be nice a fluffy and dry, but bakes, casseroles, stews, curries, etc, all are very flexible on terms of what grains you can use.
If a recipe needs a firm, dry grain, I use quinoa, millet, farro, and sorghum. For softer or more moist grain, I use couscous, oats, barley, riced cauliflower.
If I do use rice, I use brown rice because I prefer the texture.
Just play around and try different tastes and textures in different recipes. I often find couscous too sweet, quinoa too bitter, and cauliflower gets too mushy, so I learn by trial and error what will work in which recipe.