[FlightSQL][Docs] Document current state of FlightSQL support

### Describe the enhancement requested

There are plenty of ways to learn about FlightSQL [[1]](https://arrow.apache.org/docs/format/FlightSql.html#arrow-flight-sql) [[2](https://arrow.apache.org/blog/2025/02/28/data-wants-to-be-free/)] [[3](https://arrow.apache.org/adbc/current/driver/flight_sql.html)] but it's harder to find out which databases support FlightSQL and how. We have the [Powered By](https://arrow.apache.org/powered_by/) page for more general Arrow adoption but I wonder if it would be helpful if there was something specifically for FlightSQL. I think the same question could be asked for ADBC but that can be done in another ticket.

Here's a rough categorization and list I came up with after a bit of research:

via demo wrappers

- SQLite: [https://github.com/apache/arrow/blob/release-7.0.0/cpp/src/arrow/flight/sql/example/sqlite_server.h](https://github.com/apache/arrow/blob/release-7.0.0/cpp/src/arrow/flight/sql/example/sqlite_server.h), [GitHub - voltrondata/sqlflite: An example Flight SQL Server implementation - with DuckDB and SQLite back-ends.](https://github.com/voltrondata/sqlflite)
- DuckDB: [GitHub - voltrondata/sqlflite: An example Flight SQL Server implementation - with DuckDB and SQLite back-ends.](https://github.com/voltrondata/sqlflite)
- Apache Derby: [arrow/java/flight/flight-sql/src/test/java/org/apache/arrow/flight/sql/example/FlightSqlExample.java at release-7.0.0 · apache/arrow · GitHub](https://github.com/apache/arrow/blob/release-7.0.0/java/flight/flight-sql/src/test/java/org/apache/arrow/flight/sql/example/FlightSqlExample.java)

via experimental extensions

- PostgreSQL: [Apache Arrow Flight SQL adapter for PostgreSQL — Apache Arrow Flight SQL adapter for PostgreSQL current documentation](https://arrow.apache.org/flight-sql-postgresql/current/index.html)

Natively:

- Apache Doris: [Connecting by Arrow Flight SQL Protocol - Apache Doris](https://doris.apache.org/docs/db-connect/arrow-flight-sql-connect)
- CnosBD: [Arrow Flight SQL \| CnosDB](https://docs.cnosdb.com/en/docs/reference/connector/arrow_flight_sql/)
- DataFusion: [GitHub - datafusion-contrib/datafusion-flight-sql-server: DataFusion FlightSQL Server](https://github.com/datafusion-contrib/datafusion-flight-sql-server)
- Deephaven: [Connecting to a Deephaven Flight SQL server \| Deephaven](https://deephaven.io/core/docs/how-to-guides/flight-sql/)
- Denodo: [Access using Flight SQL — Virtual DataPort Developer Guide 9.1](https://community.denodo.com/docs/html/accessible/9.1/vdp/developer/access_through_flight_sql/connection_using_flight_sql/connection_using_flight_sql.html#access-using-flight-sql)
- Dremio: [Develop Applications with Arrow Flight SQL \| Dremio Documentation](https://docs.dremio.com/current/developer/arrow-flight-sql/)
- InfluxDB: [Querying InfluxDB IOx Using the New Flight SQL Plugin for Grafana \| InfluxData](https://www.influxdata.com/blog/querying-influxdb-iox-using-new-flight-sql-plugin-grafana/)
- SpiceAI: [FlightSQL \| Spice.ai Cloud Documentation](https://docs.spice.ai/building-blocks/data-connectors/flightsql)
- Theseus: [Theseus Data Processing Engine \| Voltron Data](https://voltrondata.com)

Is this categorization fair and useful and is the list accurate/complete?

If there's agreement, I think the list could be maintained at https://arrow.apache.org/docs/format/FlightSql.html#arrow-flight-sql and pages like https://arrow.apache.org/adbc/current/driver/flight_sql.html could link to this list.

cc @lidavidm @zeroshade @ianmcook

PS: Do we need/want a FlightSQL label on GitHub?

### Component(s)

Documentation, FlightRPC