For .NET only the old legacy .NET Framework, SqlClient was moved to a separate package with the rewrite (from System.Data.SqlClient to Microsoft.Data.SqlClient). They realized that it was a rather bad idea to have that baked in to your main runtime, as it complicates your updates.

For Bun you're thinking of simple key / values, hardly a database. They also have a SQLite driver which is still just a package.