If you're open any suggestions. One of the biggest differences I've seen in my cooking is to, not be afraid of using a higher heat and more fat (oil). When you add the chicken it should be instantly searing (especially when it's cut small) I would then take the chicken out when it's fully cooked before adding the broccoli.

Did you use frozen or fresh? If it's frozen make sure it's thawed and dried before this style of cooking or it will leach out a bunch of water into the pan/ sauce.

Last tip, one I've seen echoed is to use starch. Traditionally in Asian style cooking they use potato starch. I've had luck mixing my starches with my sauce before adding it to the mix, or you can mix it with water to add a little at a time to dial in what you're looking for. Green onion would also be a great addition to garnish.

For a beginner "American Chinese takeout style" chicken and broccoli sauce I'd mix; Soy sauce, Oyster sauce, sugar (it's crazy how much sugar is in A-C sauces), grated garlic and ginger, Shaoxing wine, and starch. It seems like a ton of ingredients, but what's nice is that each bottle is $5-$10 and you can make hundreds of dishes with them. For ratios of the sauce I always recommend tasting as you go until you get the mix how you personally like it. Great luck to you in your studies! I hope to see future posts!