My daughter has had multiple sleep studies done. Your doctor can refer you to a sleep specialist.
In the meantime, practice what the specialists call "sleep hygiene". No screens for an hour before bed, a cool (temperature) room, a white noise machine (for him and for you), a good routine as you said, and of course, no sugary drinks or caffeine.
Keep a journal, starting now. Keep track of his eating/drinking, his bedtime routine and times, his activities during the day, his wake-up times. A doctor will want that.
Does he take any medications or supplements or vitamins? Sometimes, vitamins can contain food colors or sugars or flavors that certain kids react to. If, for example, your son needs a vitamin for a deficiency, ask your pharmacist for a recommendation that doesn't contain food coloring or extras. If your son does take vitamins but is otherwise healthy, or eats those gummy supplements, try stopping them for a couple of weeks. If he only eats processed, microwavable foods or fast foods, consult a nutritionist (your doctor can refer you) to get your son eating healthy real foods. I'm not suggesting that he eats junk food, I'm just brainstorming any possible causes.
Does he attend school? Do his teachers notice that he's tired?
Also, check his mattress. Is it comfy? In good condition?
Hope you can figure this out!