I use a steamer basket and salt my water generously. So do restaurants. Find a steamed broccoli breakdown from a restaurant and it will have a higher sodium count than you thought.
Restaurant food = seasoning = salt = better than at home but not always better for you!
We have a winner here. I was just about to say this. Although, I think they just liberally sprinkle the salt right onto the stalks in the basket, instead of in the water.
If people knew how much salt, sugar, butter & oil was in their restaurant food, they'd eat there less often. I have a deli near me that best the best grilled cheese sandwiches. I've watched them a few times, as the grill is in front of me. They liberally spread on about a 1 1/2 - 2 tablespoons of butter
one each side of the bread. Then they night add a bit more right onto the hot grill before plopping the sandwich down. So that's FOUR - FIVE tablespoons of butter. No wonder it tastes so good!
I'm confused. If your broccoli is in a steamer basket, why do you need to salt the water when the broccoli isn't in contact with the water?
Have you ever been to the ocean? You can taste the salt water in the air, and in your mouth on a very humid day.
I swear when I eat it out, and it is fresh steamed, it is almost sweet when you bite into the stalk (there is no coating of anything on it). My broccoli tastes bitter.
Sometimes salt can bring out the sweetness. That is why salt is added to cakes & chocolate recipes. Some people sprinkle salt onto watermelon slices.
Although, they may also add sugar to the water. Maybe even soak it in sugared water for a bit.
I remember we went to the Universal Studios theme park a few times and had their fresh corn on the cob, at some buffets, which was so sweet & heavenly.

Then someone pointed out that they cook it with sugar added to the water. That was how
every cob was wonderfully sweet, no matter how many different times we went.
After that, I went home and added sugar to my water while cooking. It worked. No more tasteless cobs.
Your supplier for broccoli might be different too. Restaurants don't get the veggies that have been sitting in supermarkets, or on pallets for days before they make it to the shelves. Restaurants buy in bulk, directly from suppliers, each week. Those shipments move quickly.
Try some Farmer's Markets for fresher broccoli.