Any first-read of "The first serverless database" has the implication that the database is serverless. Comments from FaunaDB folks in this comment page clearly indicate that they mean is that it's the first database for serverless, which is a pretty bold claim, given Google and AWS and any number of other providers offer databases that are accessible from serverless things, so it essentially boils down to "The first database that's marketed specifically to serverless use cases", which is maybe true but also kindof not a useful trophy to put on the mantle?
This is further muddled by the blog post linked to from the launch announcement (https://fauna.com/blog/escape-the-cloud-database-trap-with-s...), which includes "FaunaDB Serverless Cloud is an adaptive, serverless database". Nobody is reading that and thinking "ah, an adaptive database for serverless apps".
To describe it as "The first active-active multi-cloud database", is possibly true if you mean "the first time a single company has sold a publicly-available database-as-a-service running on multiple cloud providers". But the text says "database" where "public database-as-a-service" would be the accurate term, leaving the reader with the impression that no existing databases can be set up on multiple cloud providers in an active-active HA config, which is absurd. Fixing the copy here should be pretty easy, and they're already headed in the right direction with the next bullet point, although it as well refers to "database" where it means "database-as-a-service".
It feels like somebody on marketing really wanted to have a list of firsts, so they toyed with definitions of words until they thought they could flex these into being technically accurate. I get the same feel from the closing argument in the linked blog post: "The query language, data model (including graphs and change feeds), security features, strong consistency, scalability and performance are best in class. There is no downside.". I don't think I want to trust a database if the folks designing it couldn't think of any downsides.