With timescale you still have to deal and think about database connections, nodes and what not. IMO, a truly serverless database is something like dynamodb which just gives you an HTTP endpoint and they take care of the rest.
From the blog post: "So today’s serverless data platforms are not familiar or flexible. But further, black boxes are never truly easy and worry free: you never know if there are any skeletons lurking in the proverbial closet, just waiting to cause your service to fall over."
(Timescale employee here)