Yes, CockroachDB and YugabyteDB do more than sharding, they are distributed SQL (difference here: https://dev.to/yugabyte/partitioning-vs-sharding-what-about-...). YugabyteDB is open source and has more postgres features as its query layer is a fork of postgres, but good to test both
I don't know tbh. According a post on the MongoDB community forum Transactions are built on concepts of logical sessions they require features which are only available in replica set environment. You can see more here [0]
I think callling it a gateway might be slightly correct. For example an API gateway acts as a reverse proxy to accept all API calls whilst handling traffic authentication and authorization and even things like A/B testing capabilities.
A webhooks proxy that supports both sending and receiving might be classified as a gateway.