There’s no way to embed those blocks in concrete. Besides we can see the bottom. In addition those blocks do not have mechanical attachment to the posts, the posts just fit into an indent. Even if the blocks were embedded there is zero uplift resistance.
As you’ve started to suggest the correct tie down is a foundation 18-24” deep with hold down post anchors embedded. Those anchors are then bolted to the posts. They also sell bases that get anchored into the foundation then bolted to the post. Both provide uplift capacities.
This configuration is almost as bad as it can be. The building and the fence effectively stop wind that blows in the front from escaping. This increases the pressure upward exponentially. Without a fence or building it is still a sail and needs holddowns, but those enclosures really hurt.
Things are built like this all the time and survive for a long time. However, when that gust comes the results can be not pretty. I’ve seen pergolas without roofs picked up and moved - I am assuming this will have a solid roof.