When God originally created the universe, he intended it to be a place of peace, love, and joy. There was no death or suffering. When people sinned, this brought death and suffering into the world.
So in the original creation, God provided plants that gave people all the nutrients that they needed to live. But the Flood destroyed a great deal of vegetation. It seems likely that some plants became extinct, and at the very least all the plants that we need to live would not be available everywhere. So God gave people permission to eat meat as this was now necessary to have a healthy diet.
Most Christians see this as purely a practical matter: people needed to eat meat in order to survive. There is no "lesson" here, it's just what happened. I suppose you could see the lesson that sin causes many problems, and that among these problems was the destruction of the perfect, peaceful world that God intended.
Jews and Christians routinely debate the purpose of the dietary restrictions that God gave to the Jews. Many people say that these laws were for health reasons. For example they will explain the prohibition on eating pork by saying that inadequately or improperly cooked pork can cause many diseases. Others say that the purpose wasn't any specific practical benefits, but rather that God was creating a set of rituals to set the Jews apart from other people and to remind them of their special place in his plan.
Personally I find the second theory more plausible. Just like, when we sing hymns in church, it may be that there is some health benefit to singing, exercising the lungs or whatever, but that isn't why we do it. We do it as part of a ritual to bring us closer to God.
When Noah talked about animals being clean or unclean, this apparently did not mean the same thing as when Moses talked about animals being clean or unclean. To Moses, a clean animal was one you could eat and an unclean animal was one you could not. But at the time that Noah loaded animals onto the ark, he was not allowed to eat any animals, so this could not be what the distinction meant. One theory is that clean animals were those which were used in sacrifices to God and unclean animals were those which were not. I don't know if there's any solid evidence for this or any other theory. (If someone else knows, please chime in.)
You didn't mention this, but another piece of the story is that in Acts 10:9-16, God tells Peter that the dietary laws no longer apply for Christians. Christians routinely explain this by saying that the ritual law all pointed to Christ, and now that Christ has come, it is no longer needed. In the specific context, God used the "repeal" of these rules as a lesson to Peter and the other early Jewish Christians that the Gospel was not just for Jews, but that they should be preaching to the Gentiles.
The dominion clause does not necessarily imply eating. People have uses for animals other than eating them: throughout history people have used horses, mules, and oxen to pull carts and plows; people use sheep's wool to make clothes; etc. Gen 3:21 tells us that God made Adam and Eve clothes from animal skins. It's plausible that they later made their own clothes from hides and leather.
In light of the specific statements (quoted by the OP) that God originally gave people plants to eat, and then after the flood we are told we can eat meat, it seems the most natural reading is that people were not permitted to eat meat until then. It's certainly possible that some people DID eat meat before then: the whole point of the Flood was that people weren't obeying God's laws.