You don't need to find an alternative to Neon just to get dashboards. Neon is a serverless Postgres database, not a BI tool, so no Postgres-compatible database is going to ship built-in dashboards either. You'd still need a separate reporting layer after switching.
Instead of migrating your data to a different database, you can connect Draxlr directly to your existing Neon project and build dashboards, schedule reports, and set alerts without changing where your data lives.