So, I spent some time reading the code of Woo.
For some reason, events that should trigger a refresh of cart (such as wc-blocks_added_to_cart), don't do anything to update the mini cart Woo block.
Found a way that directly calls the action to refresh the cart, with type "hack"
I kind of miss the days when you could just read the frontend JavaScript code of WooCommerce to see how you can extend it, what events to trigger and such.
Now, reading the github monorepo in code view just to figure out how to trigger addtoCart event in shop block.