01
What actually changes
Both products give you PostgreSQL. The difference is underneath: Neon separates storage from compute and branches at the storage layer; CapyDB runs an ordinary PostgreSQL process on a dedicated storage dataset and clones the dataset to branch. The consequence you will feel is that a CapyDB cell behaves like the Postgres on your laptop, because it is one.
Your schema, your queries, your extensions, and your migrations move unchanged. What needs attention is the connection layer and anything written against a provider-specific driver.