I have photos for a "how to" thread but you've started right for my method, although if you have more oats you could add them, when the oats are all turned to frass you have to decide whether to clean out the container or just add more oats. I usually only clean them out every few years myself.
On top of the oats you should add egg carton, top that with flat pieces of cardboard and add more layers ending with cardboard, creating mealworm 'condos'. I like to put holes in the cardboard and some in the egg carton for easy access for the worms and beetles. Leave one end bare so you can add food directly to the oats. Carrot and spinach/chard are staples (for the essential vitamins and minerals they contain, important when feeding to fish and reptiles, perhaps for invertebrates too) but a wide variety of vegetable and fruit scraps can be fed.
A recent innovation I stumbled upon is adding brown paper bags to the top of the enclosure. There are always enough worms and pupae in the bags that dismantling the egg cartons and digging in the substrate is not required, I get about 60ml of worms just out of the bags in each enclosure and put most of the pupae back into the bags.
I assume higher yields might be had by separating the stages but I've been doing it this way for decades without feeling I needed to. The bags I've only been adding for 5 or 6 years but it's made a big difference, no more wrecking it all and digging around, I tip the bags out onto the inverted lid, pick out all I need and pour the rest back.
One thing I've found is that particularly with new colonies they can develop a cycle where they seem to be all mostly in the same stage, all pupae, all beetles or all worms. This can be overcome by buying more worms every few weeks after setting up for a couple of months, or if you have more than one mealworm colony keeping them in different rooms (different temperatures and temperature cycles).
They are really easy to keep, I never remove food, it just gets swallowed down into the oats where any left will dry out and shrivel, I clean them out probably 3 times a decade and harvest them just by tipping out paper bags, it really couldn't be easier!