At a higher level, is this the same concept as Datomic?

Not at all, although there are some similarities at a lower level (First class notion of time). Datomic has a much tighter focus on immutability, auditability, and database-as-a-value. Datomic isn't a good fit for use as a general purpose time series db where you have billions of observations.

Noob question, what's the advantage of using a language library over using your programming language favorite http client?

Speaking with experience of the Python Stripe library, automatic type conversions, native exceptions, keeps my code cleaner.

If it were a simple API, I might agree, but Stripe does a lot of stuff and in payments, many things can go wrong. Particularly being able to directly handle exceptions (rather than picking apart obscure status codes) is a godsend.

As above, but also the out of the box HTTP client in C# is quite limited.