How to infuse flavors into steamed vegetables?
To set expectations here, you aren't going to infuse flavors into the middle of steamed vegetables and fungi, you may get some flavor penetration on the outside, but the best bet for flavored vegetables is to coat the outside with the flavor. 

When you put flavorings into water for steaming food most of the flavor stays in the water rather than getting onto the food, it's a waste of good ingredients to be honest. 

Many of the flavors you are working with are oil soluble, so your best bet would be to infuse the flavors in oil then mix with the food after steaming. A tablespoon or two of vegetable oil on low heat would be enough, you could add the garlic, pepper and ginger to the oil and cook it slowly to extract the flavors, then discard the solids. The oil could be drizzled on the vegetables. You could also go for a higher temperature method, sauteing the garlic, pepper and ginger for a short time in oil before adding your steamed vegetables to the pan and sauteing them with the flavored oil. I've used both methods, slightly preferring the second one because I like the extra flavors you get from the maillard reactions.