They got big with mysql with optimizations (maybe mariadb?). neon would be postgres aas

Vitess (sharded MySQL) is how they became relevant. But broadly they've spent a lot of time making a great DaaS. There plan is to do the same with Postgres.

Can someone explain to me the neon pricing?

5 minutes of inactivity makes it idle.

If I get one query every 5 minutes and each query takes 100ms for whole month, do I get changed for 720 hours or for 14 minutes (total compute time)?

update: It's 720 hours of compute cost. Not really serverless. It's just managed database service and it can scale to zero. That's it.